Question

The diagonal of a rectangle is √ 41 cm and its area is 20 sq. cm. The perimeter of the rectangle is:
1. 9 cm
2. 18 cm
3. 20 cm
4. 41 cm

Answer 1

Correct Answer - Option 2 : 18 cm

Explanation:

Given :

The diagonal of the rectangle is √41 cm and its area is 20 sq cm.

Formula used :

In a rectangle from Pythagorean theorem

(Diagonal)² = Length2 + breadth2

Area of rectangle = Length × breadth 

Calculations:

Given,

Diagonal of rectangle = √41 cm , Area = 20 sqcm

Let the length be 'a' and breadth be 'b' 

According to the question 

a2 + b2 = (√41)2 = 41  -- (i)

Now, 

Area of rectangle = 20 

(a × b) = 20 

⇒ b.a = 20  --- (ii)

We know

(a + b)2 = a2 + b2 + 2 ab

From (i) and (ii) ⇒ (a + b)2 = 41 + 2 × 20 = 81

⇒ a + b = 9 

Perimeter = 2 × (a + b) 

⇒ 2 × 9 ⇒ 18 cm