Pythagoras Theorem: Master Right-Angled Triangles with Interactive Quizzes

Question 1

In a right-angled triangle, which theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides?

Accepted Answer

Pythagoras' Theorem

Answer

Euclid's Theorem

Answer

Converse of Pythagoras' Theorem

Answer

Sine Rule

Question 2

Which of the following is a condition for Pythagoras' theorem to be applicable?

Accepted Answer

The triangle must be right-angled.

Answer

The triangle must be equilateral.

Answer

The triangle must have two equal sides.

Answer

The triangle must have all sides of equal length.

Question 3

In a right-angled triangle with legs of length 6 cm and 8 cm, what is the length of the hypotenuse?

Accepted Answer

12 cm

Answer

10 cm

Answer

14 cm

Answer

16 cm

Question 4

Which expression correctly represents the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

(a + b)² = c²

Question 5

Determine the length of the hypotenuse of an isosceles right-angled triangle with legs of length 5 cm.

Accepted Answer

5√2 cm

Answer

5 cm

Answer

10 cm

Question 6

Which of the following is the converse of Pythagoras' theorem?

Accepted Answer

If the square of the hypotenuse of a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled.

Answer

If a triangle has sides of length a, b, and c, and a^2 + b^2 = c^2, then the triangle is right-angled.

Answer

If a triangle is right-angled, then its sides satisfy the equation a^2 + b^2 = c^2.

Answer

If a triangle has a right angle, then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Question 7

What is the formula for the area of a right-angled triangle?

Accepted Answer

(1/2) × base × height

Answer

(1/2) × length × width

Answer

(1/2) × hypotenuse × height

Answer

(1/2) × hypotenuse × length

Question 8

Which theorem is used to find the length of the third side of a right-angled triangle when the lengths of the other two sides are known?

Accepted Answer

Pythagoras' theorem

Answer

Euler's theorem

Answer

Cosine theorem

Answer

Sine theorem

Question 9

Which side of a right-angled triangle is the longest?

Accepted Answer

The hypotenuse (the side opposite the right angle)

Answer

The side opposite the right angle

Question 10

Which of the following is the converse of the Pythagorean theorem?

Accepted Answer

If a triangle has sides of length a, b, and c, and a^2 + b^2 = c^2, then the triangle is right-angled.

Answer

If a triangle has sides of length a, b, and c, and a^2 + b^2 ≠ c^2, then the triangle is not right-angled.

Question 11

Which of the following is the correct formula for Pythagoras' Theorem?

Accepted Answer

a^2 + b^2 = c^2

Answer

a^2 - b^2 = c^2

Answer

a + b = c

Answer

a - b = c

Question 12

Which of the following is NOT a special case of Pythagoras' Theorem?

Accepted Answer

Equilateral triangle

Answer

3:4:5 triangle

Answer

45-45-90 triangle

Answer

Isosceles right-angled triangle

Question 13

In a right-angled triangle, the hypotenuse is 10 cm. If one leg is 6 cm, calculate the area of the triangle.

Accepted Answer

24 cm^2

Answer

18 cm^2

Answer

30 cm^2

Answer

36 cm^2

Question 14

The area of a right-angled triangle with legs of length 6 cm and 8 cm is:

Accepted Answer

24 cm²

Answer

12 cm²

Answer

36 cm²

Answer

48 cm²

Question 15

If the hypotenuse of a right-angled triangle is 10 cm and one of the legs is 6 cm, what is the length of the other leg?

Accepted Answer

8 cm

Answer

4 cm

Answer

6 cm

Answer

12 cm

Question 16

Given a right-angled triangle with a hypotenuse of 20 cm, and one leg measuring 12 cm. Determine the length of the other leg

Accepted Answer

16 cm

Answer

8 cm

Answer

18 cm

Answer

24 cm

Question 17

A right-angled triangle has an area of 24 cm². One of its legs is 6 cm long. Determine the length of the other leg.

Accepted Answer

12 cm

Answer

4 cm

Answer

8 cm

Answer

16 cm

Question 18

Which expression accurately represents the Pythagorean Theorem?

Accepted Answer

a² + b² = c²

Answer

a² + c² = b²

Answer

b² + c² = a²

Answer

c² - a² = b²

Question 19

Identify the triangle that cannot be right-angled using the Pythagorean Theorem.

Accepted Answer

Triangle with sides 6 cm, 8 cm, 12 cm

Answer

Triangle with sides 3 cm, 4 cm, 5 cm

Answer

Triangle with sides 5 cm, 12 cm, 13 cm

Answer

Triangle with sides 4 cm, 6 cm, 9 cm

Question 20

Which formula represents Pythagoras' Theorem accurately?

Accepted Answer

a² + b² = c²

Answer

a + b = c

Answer

c² - a² = b²

Answer

a² - b² = c

Question 21

In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the:

Accepted Answer

Other two sides

Answer

Equal sides

Answer

Adjacent sides

Answer

Opposite sides

Question 22

A ladder leans against a wall, with its base 5 feet from the wall and its top reaching a height of 12 feet. Determine the length of the ladder

Accepted Answer

13 feet

Answer

10 feet

Answer

15 feet

Answer

12 feet

Question 23

Which triangle is not a right-angled triangle?

Accepted Answer

10-10-14

Answer

3-4-5

Answer

6-8-10

Question 24

In a right-angled triangle, if the square of the hypotenuse is 169 and one leg measures 12, what is the length of the other leg?

Accepted Answer

13

Answer

11

Answer

7

Answer

15

Question 25

In a right-angled triangle with sides a, b, and c, if a² + b² = c², then the triangle is:

Accepted Answer

Right-angled

Answer

Equilateral

Answer

Obtuse-angled

Answer

Acute-angled

Question 26

Who is credited with the discovery of Pythagoras' Theorem?

Accepted Answer

Pythagoras

Answer

Aristotle

Answer

Archimedes

Answer

Euclid

Question 27

Which theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides?

Accepted Answer

Pythagoras' Theorem

Answer

Thales' Theorem

Answer

Euclid's Theorem

Answer

Descartes' Theorem

Question 28

In a right-angled triangle, the hypotenuse is twice the length of one of its legs. Determine the ratio of the length of the other leg to the length of the hypotenuse.

Accepted Answer

1:√3

Answer

3:4

Answer

1:2

Answer

2:3

Question 29

Pythagoras' Theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to:

Accepted Answer

The sum of the squares of the lengths of the other two sides

Answer

The difference of the squares of the lengths of the other two sides

Answer

The product of the lengths of the other two sides

Answer

The quotient of the lengths of the other two sides

Question 30

Which of the following sets of numbers CANNOT represent the side lengths of a right-angled triangle?

Accepted Answer

4, 5, 7

Answer

5, 12, 13

Answer

3, 4, 5

Answer

6, 8, 10

Question 31

Pythagoras' Theorem is expressed mathematically as:

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Answer

c² - b² = a²

Question 32

Calculate the length of the diagonal of a rectangular garden with a length of 10 meters and a width of 8 meters.

Accepted Answer

12.8 meters

Answer

8 meters

Answer

10 meters

Answer

15 meters

Question 33

Which of the following is the formula for Pythagoras' theorem?

Accepted Answer

a² + b² = c²

Answer

a² - b² = c²

Answer

c² - a² = b²

Question 34

In a right-angled triangle, the square of the longest side is equal to the sum of the squares of the:

Accepted Answer

Other two sides

Answer

Areas

Answer

Angles

Answer

Heights

Question 35

Which of the following is an application of Pythagoras' Theorem in real life?

Accepted Answer

Calculating the distance between two points on a map

Answer

Solving crossword puzzles

Answer

Predicting the stock market

Answer

Measuring the height of a cloud

Question 36

A right-angled triangle has sides of length 3 cm, 4 cm, and 5 cm. Which side is the hypotenuse?

Accepted Answer

5 cm

Answer

None of the above

Answer

4 cm

Answer

3 cm

Question 37

What is the length of the missing side in a right-angled triangle where one side is 12 cm and the hypotenuse is 13 cm?

Accepted Answer

5 cm

Answer

1 cm

Answer

169 cm

Answer

25 cm

Question 38

A square has a diagonal length of 10 cm. What is the length of each side of the square?

Accepted Answer

5√2 cm

Answer

5 cm

Answer

20 cm

Answer

10 cm

Question 39

A ramp is 10 meters long and rises 3 meters vertically. What is the horizontal distance covered by the ramp?

Accepted Answer

√91 meters

Answer

13 meters

Answer

10 meters

Answer

7 meters

Question 40

Which statement describes Pythagoras' theorem?

Accepted Answer

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Answer

In any triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side.

Answer

In any triangle, the square of the longest side is equal to the sum of the squares of the other two sides.

Answer

In a right-angled triangle, the square of the longest side is equal to the difference of the squares of the other two sides.

Question 41

What is the length of the hypotenuse of a right-angled triangle with legs of length 6 cm and 8 cm?

Accepted Answer

10 cm

Answer

16 cm

Answer

14 cm

Answer

12 cm

Question 42

A right-angled triangle has a hypotenuse of 13 cm and one leg is 5 cm long. What is the length of the other leg?

Accepted Answer

12 cm

Answer

6 cm

Answer

8 cm

Answer

7 cm

Question 43

A ladder is leaning against a wall. The foot of the ladder is 3 meters from the wall and the top of the ladder is 4 meters above the ground. How long is the ladder?

Accepted Answer

5 meters

Answer

4 meters

Answer

8 meters

Answer

6 meters

Question 44

Which set of numbers is NOT a Pythagorean triple?

Accepted Answer

(5, 12, 14)

Answer

(3, 4, 5)

Answer

(6, 8, 10)

Answer

(7, 24, 25)

Question 45

What is the area of a right-angled triangle with legs of length 5 cm and 12 cm?

Accepted Answer

30 cm²

Answer

25 cm²

Answer

35 cm²

Answer

40 cm²

Question 46

A rectangular garden has a length of 10 meters and a width of 8 meters. What is the length of the diagonal of the garden?

Accepted Answer

12.8 meters

Answer

10.4 meters

Answer

14.4 meters

Answer

16 meters

Question 47

Which statement is the converse of Pythagoras' theorem?

Accepted Answer

If the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is right-angled.

Answer

If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, then the triangle is right-angled.

Answer

If the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is not right-angled.

Answer

If the sum of the squares of the two shorter sides of a triangle is less than the square of the longest side, then the triangle is right-angled.

Question 48

A right-angled triangle has legs of length 3 cm and 4 cm. What is the radius of the circle inscribed in this triangle?

Accepted Answer

1 cm

Answer

1.5 cm

Answer

2.5 cm

Answer

2 cm