The length of one leg of a right triangle is 8ft.The length of hypotenuse is 4 ft longer than the other leg. What are the lengths of hypotenuse and the other leg?

Expert Answers

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Use the Pythagorean Theorem:  a^2 + b^2 = c^2, where a and b are the length of the legs and c is the hypotenuse.

Substitute 8 in for a.

8^2 + b^2 = c^2

You are given that the hypotenuse is 4 ft longer than the other leg, therefore c = b + 4.  Substitute b + 4 in for c.

64 + b^2 = (b + 4)^2

Use FOIL to expand.

64 + b^2 = b^2 + 8b + 16

Subtract b^2 from both sides.

64 = 8b + 16.

Subtract 16 from both sides.

48 = 8b

Divide both sides by 8.

6 = b

c = b + 4 = 6 + 4 = 10

length of other leg = 6 ft

length of hypotenuse = 10 ft

 

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