Similar Triangles: Finding Area Ratio from 3:4 Length Ratio

Question

Here are two similar triangles. The ratio of the lengths of the sides of the triangle is 3:4, what is the ratio of the areas of the triangles?

00:00 Find the ratio of triangle areas

00:03 Let's mark the triangles as 1,2

00:07 Find the similarity ratio

00:15 The area ratio equals the similarity ratio squared

00:24 Make sure to square both numerator and denominator

00:35 And this is the solution to the problem

Let's call the small triangle A and the large triangle B, let's write the ratio:

$\frac{A}{B}=\frac{3}{4}$

Square it:

$\frac{S_A}{S_B}=(\frac{3}{4})^2$

$\frac{S_A}{S_B}=\frac{9}{16}$

Therefore, the ratio is 9:16

9:16