# If ∆ABC is similar to ∆DEF such that ∆DEF = 64 cm^2 , DE = 5.1 cm and area of ∆ABC = 9 cm^2 . Determine the area of AB - Mathematics

Sum

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

#### Solution

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

Concept: Areas of Similar Triangles
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Exercise 7.6 | Q 1.2 | Page 94