1.

If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. Find the perimeter of the original rectangle. 1. 20 cm2. 30 cm3. 50 cm4. 60 cm

Answer» Correct Answer - Option 3 : 50 cm

GIVEN:

 length of a rectangle is decreased by 4 cm and the width is increased by 3 cm

FORMULA USED:

Area of rectangle = (l × b) sq. unit and Area of square = (side)2 sq. unit 

Perimeter of rectangle = 2(l + b) units

CALCULATION:

Let the length and breadth of the rectangle be x and y 

⇒ Area of rectangle = (l × b) sq. unit

⇒ xy cm2

⇒ new length and breadth = (x - 4) and (y + 3)

⇒ (x - 4) = (y + 3)

⇒ x - y = 7 .....(1)

⇒ Area of square = (x - 4) × (y + 3)

⇒ According to question

⇒ Area of rectangle = Area of square 

⇒ xy = (x - 4) × (y + 3)

⇒ 3x - 4y = 12 .....(2)

⇒ On solving these equation 

⇒ x = 16 and y = 9

⇒ Perimeter of rectangle = 2(l + b) units

⇒ 2(16 + 9)

⇒ 2 × 25

⇒ 50 cm

∴ perimeter of the original rectangle is 50 cm


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