Question

The area of the rectangle is equal to side of square which area is 1024 cm². If the perimeter of the rectangle is 24 cm, then find the length and breadth of the rectangle respectively.
1. 8 cm, 4 cm
2. 10 cm, 12 cm
3. 16 cm, 14 cm
4. 4 cm, 9cm
5. 10 cm, 5 cm

Answer 1

Correct Answer - Option 1 : 8 cm, 4 cm

Given - 

area of square = 1024 cm², perimeter of rectangle = 24 cm

Formula used - 

area of square = (side)²

area of rectangle = length × breadth

perimeter of rectangle = 2 × (length + breadth)

(a - b)² = (a + b)² - 4ab

Solution - 

Let the length and breadth of the rectangle be l and b respectively and side of square is a.

⇒ area of square = a² = 1024

⇒ side = a = 32 cm

⇒ According to question 

⇒ l × b = 32cm

⇒ 2 × (l + b) = 24

⇒ (l + b) = 12 cm       ----(1)

⇒ (l - b)² = (l + b)² - 4lb

⇒ (l - b)² = 144 - 4 × 32 = 16

⇒ (l - b) = 4 cm        ----(2) 

⇒ Add equation (1) and (2)

⇒ 2 × l = 16 cm

⇒ l = 8 cm

⇒ Put the values in equation (1)

⇒ b = 4 cm

∴ length = 8 cm, breadth = 4cm