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?
<pre>
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^2 + L^2 = (16 - 2L)^2}}}
{{{2L^2 =256 - 64L + 4L^2}}}
{{{0 = 4L^2 - 2L^2 - 64L + 256}}}
{{{0 = 2L^2 - 64L + 256}}}
{{{2(0) = 2(L^2 - 32L + 128)}}} ------ Factoring out GCF, 2
{{{L^2 - 32L + 128 = 0}}}
Using the quadratic equation, L = 27.3137085 (ignore), OR
L, or measure of each leg is: {{{highlight_green(highlight_green(4.6863))}}} 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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