A triangle and a parallelogram have equal area and the same base. If the height of the triangle is k times the height of the parallelogram, then what is the value of k?

Explanation

Let the common base be b. Area of triangle = \frac{1}{2} b h_t and Area of parallelogram = b h_p. Since they are equal, \frac{1}{2} b h_t = b h_p, which implies h_t = 2 h_p. Therefore, the triangle's height is 2 times that of the parallelogram, making k = 2.

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