The ratio of the perimeter of a rectangle and the perimeter of a squar

1.	The ratio of the perimeter of a rectangle and the perimeter of a square is 7 : 6. The breadth of the rectangle is equal to the side of the square. If the length of the rectangle is 40 cm, then what is the ratio of the area of the square to the area of the rectangle?1. 14 : 132. 13 : 143. 3 : 44. 4 : 35. None of these
Answer» Correct Answer - Option 3 : 3 : 4 Given: Ratio of perimeter of a rectangle and perimeter of a square = 7 : 6 Breadth of rectangle = Side of square Length of rectangle = 40 cm Formula used: (i) Perimeter of rectangle = 2(l + b) (ii) Area of rectangle = l × b Where, l = length of rectangle b = breadth of rectangle (iii) Area of square = (a)² (iv) Perimeter of square = 4a Where, a = side of square Calculation: Ratio of perimeter of a rectangle and perimeter of a square = 7 : 6 {2(l + b)}/4a = 7/6 ⇒ 12(l + b) = 28a ⇒ 12(40 + a) = 28a ⇒ 480 + 12a = 28a ⇒ 28a – 12a = 480 ⇒ 16a = 480 ⇒ a = 30 cm Area of square = (30)² ⇒ 900 cm² Area of rectangle = l × b ⇒ 40 × 30 ⇒ 1200 cm² The ratio of the area of the square to the area of rectangle = 900 : 1200 ⇒ 3 : 4 ∴ The ratio of the area of the square to the area of the rectangle is 3 : 4

The ratio of the perimeter of a rectangle and the perimeter of a square is 7 : 6. The breadth of the rectangle is equal to the side of the square. If the length of the rectangle is 40 cm, then what is the ratio of the area of the square to the area of the rectangle?1. 14 : 132. 13 : 143. 3 : 44. 4 : 35. None of these

Answer» Correct Answer - Option 3 : 3 : 4

Given:

Ratio of perimeter of a rectangle and perimeter of a square = 7 : 6

Breadth of rectangle = Side of square

Length of rectangle = 40 cm

Formula used:

(i) Perimeter of rectangle = 2(l + b)

(ii) Area of rectangle = l × b

Where,

l = length of rectangle

b = breadth of rectangle

(iii) Area of square = (a)²

(iv) Perimeter of square = 4a

Where,

a = side of square

Calculation:

Ratio of perimeter of a rectangle and perimeter of a square = 7 : 6

{2(l + b)}/4a = 7/6

⇒ 12(l + b) = 28a

⇒ 12(40 + a) = 28a

⇒ 480 + 12a = 28a

⇒ 28a – 12a = 480

⇒ 16a = 480

⇒ a = 30 cm

Area of square = (30)²

⇒ 900 cm²

Area of rectangle = l × b

⇒ 40 × 30

⇒ 1200 cm²

The ratio of the area of the square to the area of rectangle = 900 : 1200

⇒ 3 : 4

∴ The ratio of the area of the square to the area of the rectangle is 3 : 4