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In triangle ABC, AB = 15, BC = 20, and AC = 20. Find the length of the shortest altitude in this triangle.

 May 1, 2023
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Area = 1/2 * base * height Since we know the area of the triangle (we can use Heron's formula to find it), and we know the length of the base, we can solve for the height: Area = 1/2 * AC * height height = 2 * Area / AC Plugging in the values we know, we get: s = (15 + 20 + 20) / 2 = 27.5 (semiperimeter) Area = sqrt(s(s-15)(s-20)(s-20)) = 150 height = 2 * 150 / 20 = 15 Therefore, the length of the shortest altitude in this triangle is 15.
 May 1, 2023

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