# Geometry/Algebra Question

My text states the following areas of two similar triangles: $$A_1 = \frac{1}{2}h_1b$$

$$A_2=\frac{1}{2}h_2e$$

$$\frac{A_1}{A_2}=\frac{\frac{1}{2}h_1b}{\frac{1}{2}h_2e}=\left(\frac{h_1}{h_2}\right) \left(\frac{b}{e}\right)=\left(\frac{b}{e}\right) \left(\frac{b}{e}\right)=\left(\frac{b^2}{e^2}\right)$$

I'm not following how they're getting:

$$\left(\frac{h_1}{h_2}\right) \left(\frac{b}{e}\right)=\left(\frac{b}{e}\right) \left(\frac{b}{e}\right)$$

I fear it's something painfully obvious.

• The triangles are similar, so the ratio of the heights is equal to the ratio of bases. – Blue Mar 29 '14 at 13:55

For two similar triangles, the ratio of the height of the first triangle to the height of the second triangle is equal to the ratio of the base of the first triangle to the base of the second triangle.

So we have

$$\frac{h_1}{h_2}=\frac{b}{e}$$