# THE PYTHAGOREAN THEOREM WORKSHEET

Problem 1 :

Find the length of the hypotenuse in the triangle shown below.

Problem 2 :

Find the length of the leg of the right triangle shown below.

Problem 3 :

Find the area of the triangle to the nearest tenth of a meter.

Problem 1 :

Find the length of the hypotenuse of the right triangle shown below. Tell whether the side lengths form a Pythagorean triple.

Solution :

By Pythagorean Theorem, we have

(Hypotenuse)2  =  (leg)2 + (leg)2

Substitute.

x2  =  52 + 122

Simplify.

x2  =  25 + 144

x2  =  169

Take square root on each side.

x2  =  169

x  =  13

So, the length of the hypotenuse is 13 units.

Because 132  =  122 + 52, they form a Pythagorean triple.

Problem 2 :

Find the length of the leg of the right triangle shown below.

Solution :

By Pythagorean Theorem, we have

(Hypotenuse)2  =  (leg)2 + (leg)2

Substitute.

142  =  72 + x2

Simplify.

196  =  49 + x2

Subtract 49 from each side.

147  =  x2

Take square root on each side.

√147  =  x2

√147  =  x

Use product property.

√49 ⋅ √3  =  x

7√3  =  x

Hence, the required side length is 7√3 units.

Problem 3 :

Find the area of the triangle to the nearest tenth of a meter.

Solution :

We are given that the base of the triangle is 10 meters, but we do not know the height h.

Because the triangle is isosceles, it can be divided into two congruent right triangles with the given dimensions. Use the Pythagorean Theorem to find the value of h.

By Pythagorean Theorem, we have

72  =  52 + h2

Simplify.

49  =  25 + h2

Subtract 25 from each side.

24  =  h2

Take square root on each side.

√24  =  √h2

√24  =  h

Now find the area of the original triangle.

Area  =  1/2 ⋅ b ⋅ h

Substitute.

Area  =  1/2 ⋅ 10 ⋅ √24

Use calculator to approximate.

Area  =  1/2 ⋅ 10 ⋅ √24

Area  ≈  24.5 m2

Hence, the area of the triangle is about 24.5 m2.

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