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Numerade Educator

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Problem 30 Medium Difficulty

If the two equal sides of an isosceles triangle have length $ a $, find the length of the third side that maximizes the area of the triangle.

Answer

$b=\sqrt{2} a$

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Video Transcript

Okay. The first thing we know is that if science ada is h over A than H is a sign data telling us that B is to a co signed data. Remember, area is 1/2 be a trait for a triangle. So 1/2 a sign beta times to a co signed data which gives us 1/2 a squared signed to theta. Okay, we know that sign to theta is one. Therefore, the data is pi over four. Because this is true. When two pies pie over to therefore dividing it again, we have pi over four is data and remember be is to a co sign day Asako san power for would be squared of two over too, giving us be a squirt of two, okay?