the hypotenuse of a right triangle is 3m more than twice the short leg. the longer leg is 2m more than twice the shorter leg. find the lengths of the sides?

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the hypotenuse of a right triangle is 3m more than twice the short leg. the longer leg is 2m more than twice the shorter leg. find the lengths of the sides?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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s=short leg h=hypotenuse l=other leg h=3+2s l=2+2s right triangle use Pythagorean thm so h^2=l^2+s^2 (3+2s)^2=(2+2s)^2+s^2 solve for s
9+2*3*2s+4s^2=4+2*2*2s+4s^2+s^2 9+12s+4s^2=4+8s+4s^2+s^2 4s^2-4s^2-s^2+12s-8s+9-4=0 -s^2+4s+5=0 s^2-4s-5=0 (s-5)(s+1)=0 s=5 s=-1
but a leg cannot have length -1 so s=5 is the shorter leg if s=5, then h=3+2(5)=13 and l=2+2(5)=12 we can check h^2=s^2+l^2 does it? 13^2=5^2+12^2 169=25+144 169=169 so done! everything checks out!

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thank you lots =]

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