The length of the longer leg of a right triangle

Shamar Reese

Shamar Reese

Answered question

2022-05-18

The length of the longer leg of a right triangle is 16 ft more than four times the length of the shorter leg. The length of the hypotenuse is 17 ft more than four times the length of the shorter leg.
Please, find the side lengths of the triangle.

Answer & Explanation

Rubi Boyle

Rubi Boyle

Beginner2022-05-19Added 14 answers

The length of the longer leg is 16 Ft more than four times the length of the shorter leg. And the length of hypotenuse is 17 Ft more than four times of the shorter leg
Thus, let the shorter leg be x
The longer leg be 4 x + 16
The hypotenuse be 4 x + 17

Now, by the Pythagorean theorem we have:
x 2 + ( 4 x + 16 ) 2 = ( 4 x + 17 ) 2
x 2 + 16 x 2 + 128 x + 256 = 16 x 2 + 136 x + 289
x 2 + 128 x 136 x + 256 289 = 0
x 2 8 x 33 = 0
x 2 11 x + 3 x 33 = 0
x ( x 11 ) + 3 ( x 11 ) = 0
( x 11 ) ( x + 3 ) = 0
Either x 11 = 0 or x + 3 = 0
x = 11 or x = 3
As, it’s not possible for x = 3 to be the length of the leg (it’s negative), the length of shorter leg is 11 Ft

Therefore,
Length of the shorter leg = 11 F t
Length of the longer leg = ( 4 × 11 + 16 ) = 60 F t
Length of the hypotenuse = ( 4 × 11 + 17 ) = 61 F t

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