Question

B

Answer 1

Answers:  

hypotenuse = 20 feet

longer leg = 16 feet

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Explanation:

c = x = length of the hypotenuse

a = x-4 = length of one of the legs

b = 12 = length of the other leg

Use the pythagorean theorem

a^2 + b^2 = c^2

12^2 + (x-4)^2 = (x)^2

144 + x^2 - 8x + 16 = x^2

144 - 8x + 16 = 0 .... the x^2 terms cancel

160-8x = 0

160 = 8x

8x = 160

x = 160/8

x = 20 is the hypotenuse

x-4 = 20-4 = 16 is the longer leg

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Check:

12^2+16^2 = 144+256 = 400

20^2 = 400

Since 12^2+16^2 = 20^2 is true, this means we have a right triangle with legs of 12 and 16, while the hypotenuse is 20. The answer is confirmed.