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# Geometry

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The lengths of two sides of ABC are 15 and 20, and the triangle area is 150. What is the perimeter of ABC?

Thank you :)

Feb 22, 2021

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At first glance, it seems like Heron's formula is needed, but notice that $$\frac{15\cdot20}{2} = 150$$. That means 15 and 20 are the length of the legs of a right triangle.

The hypotenuse of that triangle is $$\sqrt{15^2+20^2}=25$$, using the Pythagorean theorem.

The perimeter of ABC is therefore equal to $$15+20+25=\boxed{60}$$

Feb 22, 2021