Question 206204
For a triangle, {{{A=(1/2)bh}}}
Because it is a right triangle, the two legs are the base and height.
let x = the shorter leg
2x+4 = the longer leg
{{{120 = (1/2)(x)(2x+4)}}}
{{{240=2x^2+4x}}}
{{{2x^2+4x-240=0}}}
Divide by 2.
{{{x^2+2x-120=0}}}
Factor.
{{{(x+12)(x-10)=0}}}
{{{(x+12)=0}}} or {{{(x-10)=0}}}
{{{x=-12}}} or {{{x=10}}}
The side length canot be negative, so ignore {{{x=-12}}}
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The shorter leg has length 10in, and the longer leg has length {{{2(10)+4}}} = 24in