Question

The breadth and length of two rectangles are in the ratio 2 : 3. In another rectangle, whose breadth is 1 cm less and length is 3 cm less than those of the first, this ratio is 3 : 4. Calculate the breadth and length of both rectangles.

Answer 1

Ratio between the breadth and length of the first rectangle = 2 : 3

Breadth of the first rectangle = 2x

Length of the first rectangle = 3x

Breadth of the second rectangle = 2x – 1

Length of the second rectangle = 3x – 3

Ratio between the breadth and length = 3 : 4

so, (2x – 1) : (3x – 3) = 3 : 4

3 (3x – 3) = 4 (2x – 1)

9x – 9 = 8x – 4

9x – 8x = -4 + 9

x = 5

Breadth of the first rectangle = 2x = 2 × 5 = 10 cm

Length of the first rectangle = 3x = 3 × 5 = 15 cm

Breadth of the second rectangle = 2x – 1 = 10 – 1 = 9 cm

Length of the second rectangle = 3x – 3 = 15 – 3 = 12 cm