A triangle with sides 4 and 16 draws the heights to these sides. The height drawn to the first side is 4

bystudin | May 31, 2020 | Education

A triangle with sides 4 and 16 draws the heights to these sides. The height drawn to the first side is 4. What is the height drawn to the second side?

Let AB be the side of length 4 and AC the side of length 16.
The problem is easily solved through the area of the triangle.
The area of the triangle is equal to half the product of the height and the side to which the height is drawn. Hence:
S = AB * CD / 2 = 4 * 4/2 = 8
Also: S = AC * BE / 2
8 = 16 * BE / 2
16 = 16 * BE
BE = 1
Answer: 1

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