Question

The perimeter of the top of a rectangular table is 28 cm, whereas its area is 48 cm².What is the length of its diagonal? 
1. 10
2. 12.5
3. 20
4. 12

Answer 1

Correct Answer - Option 1 : 10

Given:

The perimeter of the top of a rectangular table is 28 cm

The area is 48 cm²

Formula used:

The perimeter of a rectangle is 2(L + B)

The area of a rectangle is L × B

where L = length, B = breadth

The diagonal of a rectangle is √(L² + B²)

Calculation:

The perimeter of a rectangle = 28 cm

The Area of a rectangle = 48 cm²

According to the question, we get

⇒ 2(L + B) = 28

⇒ L + B = 14

And 

L × B = 48

Now,

(L + B)² = L² + B² + 2LB

⇒ (14)² = L² + B² + 2 × 48

⇒ 196 - 96 = L² + B²

⇒ L2 + B² = 100 = (10)²

∴ The length of the diagonal is 10.