Practice the questions of **McGraw Hill Math Grade 8 Answer Key PDF Lesson 20.3 Right Triangles and Pythagorean Theorem **to secure good marks & knowledge in the exams.

## McGraw-Hill Math Grade 8 Answer Key Lesson 20.3 Right Triangles and Pythagorean Theorem

**Exercises**

**SOLVE**

**Use the Pythagorean Theorem to determine the length of the missing side.**

Question 1.

If side A is 6 and side B is 8, then side C (the hypotenuse) is _____________

Answer:

C = 10,

Explanation:

As side A is 6 and side B is 8, then side C (the hypotenuse) is applying Pythagorean theorem that is theÂ square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A^{2 }+ B^{2 }) = square root of (6^{2 }+ 8^{2})= square root of (36 + 64) = square root of 100 = 10.

Question 2.

If side A is 9 and side B is 9, then side C (the hypotenuse) is _____________

Answer:

C = 12.72,

Explanation:

As side A is 9 and side B is 9, then side C (the hypotenuse) is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A^{2 }+ B^{2 }) = square root of (9^{2 }+ 9^{2})= square root of (81 + 81) = square root of 162 , approximately equal to 12.72.

Question 3.

If side A is 10 and side B is 24, then side C (the hypotenuse) is _____________

Answer:

C = 26,

Explanation:

As side A is 10 and side B is 24, then side C (the hypotenuse) is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A^{2 }+ B^{2 }) = square root of (10^{2 }+ 24^{2})= square root of (100 + 576) = square root of 676 = 26.

Question 4.

If side A is 9 and side C (the hypotenuse) is 15, then side B is _____________

Answer:

B = 12,

Explanation:

As side A is 9 and side C (the hypotenuse) is 15, then side B is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. C = square root of (A^{2 }+ B^{2 }) therefore B = square root of (C^{2 –}Â A^{2})= square root of (225 – 81) = square root of 144 = 12.

Question 5.

If side B is 6 and the hypotenuse is 10, then side A is _____________

Answer:

A = 8,

Explanation:

As side B is 6 and the hypotenuse is 10, then side A is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A^{2 }+ B^{2 }) therefore A = square root of (C^{2 }– B^{2})= square root of (100 – 36) = square root of 64 = 8.

Question 6.

If side A is 12 and side B is 5, then side C (the hypotenuse) is _____________

Answer:

C = 13,

Explanation:

As side A is 12 and side B is 5, then side C (the hypotenuse) is applying Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So C = square root of (A^{2 }+ B^{2 }) = square root of (12^{2 }+ 5^{2}) = square root of (144 + 25) = square root of 169 = 13.

**Find the missing sides of the following pairs of similar right triangles:**

Question 1.

HI = ___________ ft

KL = ___________ ft

JL = ____________ ft

Answer:

HI = 50 ft.,

KL = 30 ft.,

JL =Â 78 ft.,

Explanation:

For finding HI we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So HI = square root of (GI^{2 }– GH^{2 }) = square root of (130^{2 }– 120^{2}) = square root of (16,900 – 14,400) = square root of 2,500 = 50 ft.

Now finding KL let it be x as GHI and JKL are similar triangles that means the ratios of the sides are equalÂ HI/GH = KL/JK = 50/120 = x/72 cross multiplying for the unknown we get

120x = 50 X 72, x = 5 X 72/12 = 5 X 6 = 30 ft.

Now JL we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So HI = square root of (JK^{2 }+ KL^{2 }) = square root of (72^{2 }+ 30^{2}) = square root of (5,184 + 900) = square root of 6,084 = 78 ft.

Question 2.

LN = ___________ m

PQ = ___________ m

OQ = ____________ m

Answer:

LN = 25 ft., = 7.62 m,

PQ = 21 ft., = 6.4008 m,

OQ = 35 ft., = 10.668 m,

Explanation:

For finding LN we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So LN = square root of (LM^{2 }+ MN^{2 }) = square root of (20^{2 }+ 15^{2}) = square root of (400 + 225) = square root of 625 = 25 ft. As 1 foot is equal to 0.3048 meter,

so 25 X 0.3048 m = 7.62 m.

Now finding PQ let it be x as LMN and OPQ are similar triangles that means the ratios of the sides are equalÂ MN/LM = PQ/OP = 15/20 = x/28 cross multiplying for the unknown we get

20x = 15 X 28, x = 3 X 28/4 = 3 X 7 = 21 ft., = 21 X 0.3048 m = 6.4008 m.

Now OQ we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So OQ = square root of (OP^{2 }+ PQ^{2 }) = square root of (28^{2 }+ 21^{2}) = square root of (784 + 441) = square root of 1,225 = 35 ft., = 35 X 0.3048 m =Â 10.668 m.

Question 3.

RT = ___________ in.

VW = ___________ in.

UW = ____________ in.

Answer:

RT = 7.071 ft., = 84.852 in.,

VW = 20 ft., = 240 in.,

UW = 28.284 ft., = 339.400 in.,

Explanation:

For finding RT we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So HI = square root of (RS^{2 }+ ST^{2 }) = square root of (5^{2 }+ 5^{2}) = square root of (25 + 25) = square root of 50 = 7.071 ft. As 1 foot is equal to 12 inch we get 7.071 X 12 inch = 84.852 in, Now finding VW let it be x as RST and UVW are similar triangles that means the ratios of the sides are equalÂ ST/RS = VW/UV = 5/5 = x/20 cross multiplying for the unknown we get 5x = 5 X 20, x = 20 ft., = 20 X 12 in = 240 in.,

Now UW we apply Pythagorean theorem that is the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides. So UW = square root of (UV^{2 }+ VW^{2 }) = square root of (20^{2 }+ 20^{2}) = square root of (400 + 400) = square root of 800 = 28.284 ft., = 339.408 in.

Question 4.

If the two triangles are similar, then what is the length of the missing side?

Answer:

The length of the missing side is 16 ft.,

Explanation:

As given two triangles are similar triangles that means the ratios of the sides are equal, Let the missing side be x so 9/12 = 12/x cross multiplying for the unknown we get 9x = 12 X 12, x = 12 X 12/9 = 12 X 4 /3 = 4 X 4 = 16 ft.