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Geometry

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Triangle ABC is isosceles with AB = BC. If AC = 20 and [ABC] = $$280$$, then find the perimeter of triangle ABC.

Feb 11, 2022

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Since triangle ABC is isosceles with AB = BC, then AC is the base of the triangle. If the area is 280, then base x height = 560, plugging in the values, 20 x height = 560. Thus, the height is 28.

The height of triangle ABC is also the perpendicular bisector of the triangle. Thus, the point that the height meets the base will be called point D. So AD = AC/2 = 10. Using the pythagorean theorem, AB^2 = AD^2 + BD^2, so AB^2 = 100 + 784 = 884.

AB = $$2\sqrt{221}$$. AB = BC so the perimeter of triangle ABC is $$20 + 4\sqrt{221}$$.

Feb 12, 2022