Question

The length of a rectangle is thrice its breadth and the length of its diagonal is `8sqrt(10)` cm. The perimeter of the rectangle is ______.

Options

• `15sqrt(10)` cm

• `16sqrt(10)` cm

• `24sqrt(10)` cm

• 64 cm

Answer 1

The length of a rectangle is thrice its breadth and the length of its diagonal is `8sqrt(10)` cm. The perimeter of the rectangle is 64 cm.

Explanation:

Let the breadth be x cm.

Then, length = 3x cm.

∴ Diagonal = `sqrt((3x)^2 + x^2)  cm`

= `xsqrt(10)  cm`

Thus, `xsqrt(10) = 8sqrt(10)`

⇒ x = 8

Perimeter = 2(3x + x) cm

= 8x cm

= (8 × 8) cm

= 64 cm