SOLUTION: One leg of a right triangle is 7cm shorter than the other leg. How long should the shorter leg be to ensure that the hypotenuse is at least 13cm?

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Question 1153637: One leg of a right triangle is 7cm shorter than the other leg. How long should the shorter leg be to ensure that the hypotenuse is at least 13cm?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if one leg of a right triangle is 7cm shorter than the other leg, we have
a=b%2B7
if the hypotenuse is at least 13cm, then
a%5E2%2Bb%5E2=13%5E2....substitute a
%28b%2B7%29%5E2%2Bb%5E2=13%5E2
b%5E2%2B14b%2B49%2Bb%5E2=169
2b%5E2%2B14b%2B49-169=0
2b%5E2%2B14b-120=0
b%5E2%2B7b-60=0.....factor
b%5E2%2B12b-5b-60=0
%28b%5E2%2B12b%29-%285b%2B60%29=0
b%28b%2B12%29-5%28b%2B12%29=0
%28b+-+5%29+%28b+%2B+12%29+=+0
=> b=5 or b=-12->disregard negative solution
so, a=b%2B7->a=5%2B7->a=12