Question

If the breadth and perimeter of a rectangle are in the ratio 1 : 8 and the area of rectangle is 363 cm², then the breadth of the rectangle is:
1. 11 cm
2. 13 cm
3. 12 cm
4. 10 cm

Answer 1

Correct Answer - Option 1 : 11 cm

Given:

Ratio of breadth and perimeter of rectangle = 1 : 8

Area of the Given rectangle = 363 cm²

Formula Used:

Perimeter of rectangle = 2(length + breadth)

Area of Rectangle = length × breadth

Calculation:

Let the breadth be 1x and perimeter be 8x

Length of rectangle = l cm

Breadth of rectangle = b cm

2(l + b) = 8x

⇒ 2(l + x) = 8x

⇒ 2l = 8x – 2x = 6x

⇒ l = 3x cm

Now,

3x × x = 363 cm²

⇒ 3x² = 363 cm²

⇒ x = √121 cm

⇒ x = 11 cm

Since x is the value of breadth of rectangle therefore,

Breadth = x = 11 cm

∴ The Breadth of Rectangle is 11 cm.