∆ABC is similar to ∆DEF. Find the ratio between ∆DEF and ∆ABC. Express the answer as a fraction in simplest form

Question

∆ABC is similar to ∆DEF. Find the ratio between ∆DEF and ∆ABC. Express the answer as a fraction in simplest form

Answer 1

The ratio between the areas of two similar triangles is equal to the square of the ratio between their corresponding side lengths.

Let's assume that the corresponding side lengths are AB and DE. Then, the ratio between the lengths of their corresponding sides is AB/DE.

Therefore, the ratio between the areas of ∆ABC and ∆DEF is (AB/DE)^2.

Since we want the ratio to be expressed as a fraction in simplest form, we should simplify (AB/DE)^2.

Hence, the ratio between ∆DEF and ∆ABC is AB^2/DE^2.