SOLUTION: 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?

Algebra ->  Parallelograms -> SOLUTION: 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?       Log On


   

Question 859379: 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?
Answer by Awesom3guy(31) About Me  (Show Source):
You can put this solution on YOUR website!
When you are having trouble with this, it helps when you draw it.
Let's call the height of the parallelogram p and the one of the triangle t.

Both of their bases are the same length. Let's call that B.

The area of a parallelogram is base*height, and of the triangle is HALF of its own (base*height).

The two areas are the same, and so are the bases, and what is different are the heights. So you set up:

B%2Ap+=+B%2At%2F2
As B can be cancelled (same value on numerators on both sides, you have this:

p+=+t%2F2
So we can say that - height of the parallelogram is half of the one of triangle, or, if we multiply the equation with 2
t+=+2p
Height of the triangle is double the height of the parallelogram.