Question

The area of a rectangle is 168 cm² and the perimeter is 62 cm, then the length of the diagonal is?
1. 23√6 cm
2. 12 cm
3. 25 cm
4. 18√3 cm

Answer 1

Correct Answer - Option 3 : 25 cm

Given:

The area of a rectangle is 168 cm2

The perimeter of a rectangle is 62 cm

Formula Used:

Area of rectangle = length × breadth

Perimeter of rectangle = 2(length + breadth)

As the sides of a rectangle are perpendicular, 

⇒ d² = l² + b²,

d is diagonal of a rectangle,

l is the length of a rectangle,

b is the breadth of a rectangle

(x + y)² = x² + y² + 2xy

Calculation:

Let the length and the breadth be 'l' and 'b' respectively.

The area of a rectangle is 168 cm2

⇒ l × b = 168 cm²

The perimeter of a rectangle is 62 cm

⇒ 2 (l + b) = 62

⇒ l + b = 31

Now,

(l + b)² = l² + b² + 2lb 

⇒ (31)² =l2 + b2 + 2(168)

⇒ 961 = l2 + b2 + 336

⇒  l2 + b2 = 961 – 336

⇒  l2 + b2 = 625

As the sides of a rectangle are perpendicular, 

⇒ d2 = l2 + b2,

⇒ d2 = 625

⇒ d = √625

⇒ d = 25

∴ Diagonal of a rectangle is 25 cm.