The base of a parallelogram and a triangle are the same length, and both figures have the same area. What is true about height of the triangle?a. It is the same as the parallelogram's height.b. It is half of the parallelogram's height.c. It is twice the parallelogram's height. d. Its height is twice its base.

Accepted Solution

Recall that the area of a triangle is [tex]\frac12bh[/tex] and the area of a parallelogram is [tex]bh[/tex].

The bases, [tex]b[/tex], are equal, but the heights, [tex]h[/tex] are not necessarily.  Let us use [tex]h_t[/tex] to denote the height of the triangle and [tex]h_p[/tex] to denote the height of the parallelogram.

The areas of the triangle and the parallelogram are equal: [tex]\frac12bh_t=bh_p[/tex].  Thus [tex]\frac12h_t=h_p[/tex] and [tex]h_t=2h_p[/tex].

That is, the height of the triangle is twice the height of the parallelogram.  The answer is c.