SOLUTION: The longer leg of a right triangle is 6 cm longer than 6 times the shorter leg and also 1 cm shorter and the hypotenuse. Find the perimeter of the triangle.

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Question 142477This question is from textbook Algebra Structure and Method Book 1
: The longer leg of a right triangle is 6 cm longer than 6 times the shorter leg and also 1 cm shorter and the hypotenuse. Find the perimeter of the triangle. This question is from textbook Algebra Structure and Method Book 1

Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
let x=shorter

"The longer leg of a right triangle is 6 cm longer than 6 times the shorter leg" __ 6x+6

"and also 1 cm shorter (than) the hypotenuse" __ 6x+7

(x)^2+(6x+6)^2=(6x+7)^2 __ x^2+36x^2+72x+36=36x^2+84x+49 __ x^2-12x-13=0

factoring __ (x-13)(x+1)=0 __ x=13 and x=-1 __ negative value not realistic

perimeter=13+6(13)+6+6(13)+7 __ p=182