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
1. 105
2. 145
3. 100
4. 135
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.