Application of Proportions

Question

how to solve: A right triangle has an area of 13m^2. The diamensions of the triangle are increased by a scale factor of 3. What is the area of the new triangle?

I Don't Need The Aswer, Just How To Solve It.

Thanks :D

Answer 1

When the dimensions of the triangle are multiplied by a scale factor of 3, this means that the lengths of each of the triangle's sides are being multiplied by 3. The equation for the area of a triangle is (1/2)(base)(height). We can set this equal to A1. When the triangle is increased by a scale factor of 3, the height of the triangle is also increased by a scale factor of 3 because they are similar triangles. taking this into consideration, A2= (1/2)([3][base])([3][height])=(9/2)(base)(height) and since we know that A1=(1/2)(base)(height) then using the equation for A2 we can conclude that (A1)(9)=A2 or (13)(9)=117.