SOLUTION: The shorter leg of a right triangle is 17cm less than the longer leg.. If the hypotenuse is 25ch long,find the perimeter of the triangle

Question 547097: The shorter leg of a right triangle is 17cm less than the longer leg.. If the hypotenuse is 25ch long,find the perimeter of the triangle
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
The shorter leg of a right triangle is 17cm less than the longer leg.. If the hypotenuse is 25ch long,find the perimeter of the triangle
Let x = longer leg
then
x-17 = shorter leg
.
Applying Pythagorean theorem:
x^2 + (x-17)^2 = 25^2
x^2 + (x-17)(x-17) = 25^2
x^2 + x^2-34x+289 = 625
2x^2-34x+289 = 625
2x^2-34x-336 = 0
x^2-17x-168 = 0
(x+7)(x-24) = 0
x = {-7, 24}
throw out the negative solution leaving:
x = 24 cm (longer leg)
.
shorter leg:
x-17 = 24-17 = 7 cm
.
perimeter = 24+7+25 = 56 cm
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