In a triangle with sides 2 and 4, the heights to these sides are drawn. The height drawn to the first side is 2.

In a triangle with sides 2 and 4, the heights to these sides are drawn. The height drawn to the first side is 2. What is the height drawn to the second side?

Let AB be a side of length 2 and AC the side of length 4.
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 = 2 * 2/2 = 2
Also: S = AC * BE / 2
2 = 4 * BE / 2
4 = 4 * BE
BE = 1
Answer: 1

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