SOLUTION: The length of one lege of a right triangle is 7" more than the length of the shorter leg. If the hypotenuse is 7" more that the longer leg, FIND the are of the triangle

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Question 352231: The length of one lege of a right triangle is 7" more than the length of the shorter leg. If the hypotenuse is 7" more that the longer leg, FIND the are of the triangle
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the shortest leg be x.
x%5E2%2B%28x%2B7%29%5E2=%28x%2B14%29%5E2
x%5E2%2Bx%5E2%2B14x%2B49=x%5E2%2B28x%2B196
2x%5E2%2B14x%2B49=x%5E2%2B28x%2B196
x%5E2-14x-147=0
Factor
%28x-21%29%28x%2B7%29=0
Only the positive solution makes sense in this problem.
x-21=0
x=21inches
.
.
.
A=%281%2F2%29x%28x%2B7%29
A=%281%2F2%29%2821%29%2828%29
highlight%28A=294%29sq.in.