The difference between the areas of a rectangle and square is 35 cm2.

1.	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. 1052. 1453. 1004. 135
Answer» 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.

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. 1052. 1453. 1004. 135

Answer» 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.