# geometry

the area of a right triangle is 12 in ^2. the ratio of the lengths of its legs is 2/3. find the hypotenuse.

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1. Let the shortest leg length be a.

Area = (a)*(3a/2)*(1/2) = (3/4)a^2 = 12
a^2 = 16
a = 4 and the other leg (which we'll call b) must be 6.

Use the Pythagorean theorem for the hypotenuse, c.
c^2 = a^2 + b^2

c = sqrt(52) = 7.2111 inch

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