Question
Asked Jun 26, 2019
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The length of the longer leg of a right triangle is
13
inches

more than three times the length of the shorter leg. The length of the hypotenuse is
14
inches

more than three times the length of the shorter leg. Find the side lengths of the triangle.

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Expert Answer

Step 1

Let the length of shorter leg be x.

Then the length of the longer leg will be 13+3x.

The length of the hypotenuse will be 14+3x.

 According to the pythogrus theorem,

(hypotenuse) (shoter leg) +(longerleg)
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(hypotenuse) (shoter leg) +(longerleg)

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Step 2

Substitute  the values.

(14+3x(x (13+3x)
196+84x +9x2 x2 +169+ 78x +9x2
196 84x x2 +169 +78x
x26x27 0
x-9x3x 27 = 0
(x-9)(x+3) 0
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(14+3x(x (13+3x) 196+84x +9x2 x2 +169+ 78x +9x2 196 84x x2 +169 +78x x26x27 0 x-9x3x 27 = 0 (x-9)(x+3) 0

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Step 3

 Equate each fa...

(x-9) 0 or (x+3) 0
x = -3
or
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(x-9) 0 or (x+3) 0 x = -3 or

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