Question

The difference between the areas of a rectangle and square is 35 cm². If the rectangle’s length and breadth are 50% more and 10% less respectively than the side of the square, what is the area of the rectangle? (in cm²)
1. 105
2. 145
3. 100
4. 135

Answer 1

Correct Answer - Option 4 : 135

Given:

The difference between the areas of a rectangle and square = 35 cm

Formula used:

Area of rectangle = length × breadth

Area of square = (side)²

Calculation:

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

The length of a rectangle(l) = [(100 + 50)/100] × a

⇒ [150/100] × a

⇒ 1.5a

The breadth of a rectangle(b) = [(100 – 10)/100] × a

⇒ [90/100] × a

⇒ 0.9a

The difference between the areas of a rectangle and square = 35 cm

⇒ length × breadth – (side)2 = 35

⇒ 1.5a × 0.9a – a² = 35

⇒ 1.35 × a2 – a² = 35

⇒ 0.35 × a² = 35

⇒ a2 = 35/0.35

⇒ a2 = 100

⇒ a = 10 cm

The length of a rectangle = 1.5a

⇒ 1.5 × 10

⇒ 15 cm

The breadth of a rectangle = 0.9a

⇒ 0.9 × 10

⇒ 9 cm

The area of a rectangle = 15 × 9

⇒ 135 cm² 

∴ The area of a rectangle is 135 cm2.