Question

1. the ratio of the areas of two similar triangles is 100:64. what is the ratio of the lengths of corresponding sides (big to small)?

Explanation:

Step1: Recall area-side ratio rule

For similar figures, the ratio of areas ($AR$) is the square of the ratio of corresponding side lengths ($SR$). So $AR = (SR)^2$.

Step2: Substitute given area ratio

We know $AR = \frac{100}{64}$, so $\frac{100}{64} = (SR)^2$.

Step3: Solve for side length ratio

Take the positive square root of both sides (since lengths are positive):
$SR = \sqrt{\frac{100}{64}} = \frac{\sqrt{100}}{\sqrt{64}} = \frac{10}{8} = \frac{5}{4}$

Answer:

The ratio of the lengths of corresponding sides (big to small) is $\frac{5}{4}$ or $5:4$