If a triangle has a perimeter of 18 inches and you double the dimensions, what will that do to the area? To the perimeter? Explain.

Answer 1

Doubling the perimeter of a triangle will also double its height. You can show this pretty easily using the Pythagorean Theorem or by using similar triangles and the associated ratios.

Thus the new area will be 1/2 * (2b) * (2h) = 4 * (1/2 bh), or four times the area of the original triangle.

In general, scaling a triangle by a factor of k will increase its area by a factor of k^2::

1/2 * (kb) * (kh) = k^2 * (1/2 bh),