SOLUTION: In an isosceles right triangle, the legs are 3 inches smaller than the hypotenuse. If the perimeter is 16 inches, how long are the legs of the triangle?

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Question 898895: In an isosceles right triangle, the legs are 3 inches smaller than the hypotenuse. If the perimeter is 16 inches, how long are the legs of the triangle?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
x for leg
h for hypotenuse
x=h-3, if the description about this is understood correctly.

Expect because of right, isosceles, that x%5E2%2Bx%5E2=h%5E2 applying Pythagorean Theorem.
2x%5E2=h%5E2.

Perimeter is given, 16.
x%2Bx%2Bh=16
2x%2Bh=16

A system of two equations is now possible.
system%282x%5E2=h%5E2%2C2x%2Bh=16%29.

h=16-2x
h=2%288-x%29
substitute into the Pythagorean simplified equation;
2x%5E2=%282%288-x%29%29%5E2
2x%5E2=4%288-x%29%5E2
x%5E2=2%288-x%29%5E2
x%5E2=2%2864-18x%2Bx%5E2%29
x%5E2=128-36x%2Bx%5E2
0=128-36x
36x=128
x=128%2F36
highlight%28x=32%2F9%29

Use the perimeter fact to find h, the hypotenuse.
h=16-2x
h=16-2%2832%2F9%29
h=%2816%2A9-2%2A32%29%2F9
h=%28144-64%29%2F9
highlight%28h=80%2F9%29

Is h-x=3?
80%2F9-32%2F9
%2880-32%29%2F9
48%2F9
highlight_green%28h-x=5%261%2F3%3C%3E3%29-----That part of the problem description is WRONG.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
In an isosceles right triangle, the legs are 3 inches smaller than the hypotenuse. If the perimeter is 16 inches, how long are the legs of the triangle?


Let measure of each leg, be L

Then total length of two legs = 2L

Since perimeter = 16, then hypotenuse = 16 – 2L

As this is a right-triangle, we get: L%5E2+%2B+L%5E2+=+%2816+-+2L%29%5E2

2L%5E2+=256+-+64L+%2B+4L%5E2

0+=+4L%5E2+-+2L%5E2+-+64L+%2B+256

0+=+2L%5E2+-+64L+%2B+256

2%280%29+=+2%28L%5E2+-+32L+%2B+128%29 ------ Factoring out GCF, 2

L%5E2+-+32L+%2B+128+=+0

Using the quadratic equation, L = 27.3137085 (ignore), OR

L, or measure of each leg is: highlight_green%28highlight_green%284.6863%29%29 inches

Are you certain you copied this problem correctly? There doesn't seem to be a measurement for each leg

that will is 3 inches less than the hypotenuse.

You can do the check!! 



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