What will be the length of the diagonal of that square plot whose area is equal to the area of a rectangular plot of length 64 m and breadth 49 m?

A 45 m

B \(45\sqrt 2 \;m\)

C 56 m

D \(56\sqrt 2 \;m\)

E None of these

Correct Answer: Option D

Area of Rectangle = Length × Breadth

⇒ Area of Rectangle = 64 × 49

Given : Area of Rectangle = Area of Square

let the side of the square be "a"

Area of square with side "a" = a²

⇒ Area of Rectangle = 64 × 49= Area of Square = a²

⇒a = \(\sqrt {(64 \times 49}\) = 8×7 = 56 m

The length of the diagonal of the square with side a is a \(\sqrt 2\)

⇒ length of the diagonal of the square is 56\(\sqrt 2\)

Hence Option (4)