Question

If ∆ABC is similar to ∆DEF such that ∆DEF = 64 cm² , DE = 5.1 cm and area of ∆ABC = 9 cm² . Determine the area of AB

Answer 1

Since the ratio of areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

`\therefore \text{ }\frac{Area\ (\Delta ABC)}{Area\,\,(\Delta DEF)}=(AB^2)/(DE^2)`

`\Rightarrow \frac{9}{64}=(AB^2)/(5.1)^2`

`\Rightarrow AB=\sqrt{3.65}`

⇒ AB = 1.912 cm