Question

The perimeter of the rectangular field is 62 m and its area is 168 m². What is the diagonal of the rectangular field?
1. 21 m
2. 25 m
3. 24 m
4. 23 m

Answer 1

Correct Answer - Option 2 : 25 m

Given:

The perimeter of the rectangular field is 62 m

The area of the rectangular field = 168 m2

Formula used:

The perimeter of the rectangle = 2(l + b)

The area of the rectangle = lb

The diagonal of the rectangle = √(l² + b²)

Here, l → Length, b → Breadth

Calculation:

Perimeter of the rectangular field = 62

⇒ 2(l + b) = 62 

⇒ (l + b) = 31      ---(1)

Area of the rectangular field = 168

⇒ lb = 168      ---(2)

Now, squaring eq (1)

(l + b)² = 31²

⇒ l² + b² + 2lb = 961

⇒ l2 + b2 + 2 × 168 = 961

⇒ l2 + b2 = 961 - 336

⇒ l2 + b2 = 625

The diagonal of the rectangular field = √(l2 + b2)

⇒ √625 = 25      ---(Neglecting -ve value)

∴ The diagonal of the rectangular field is 25 cm