Question

If the adjacent sides of a rectangle are in the ratio \(1\tfrac{2}{3}\):\(3\tfrac{2}{4}\), and its perimeter is 248 cm, then its area is (in sq. cm): 

1. 3320
2. 3360
3. 3340
4. 3660

Answer 1

Correct Answer - Option 2 : 3360

Given:

The ratio of adjacent sides of a rectangle = \(1\tfrac{2}{3}:3\tfrac{2}{4}\)

⇒ 5/3 : 14/4

⇒ 10 : 21

Perimeter of rectangle = 248 cm

Formula used:

Perimeter of rectangle = 2(l + b)

Area of rectangle = lb

Calculation:

Suppose the adjacent sides of rectangle is 10x and 21x, respectively.

Therefore, 2(l + b) = 248

⇒ 2(10x + 21x) = 248

⇒ 31x = 124

⇒ x = 4

Therefore, l = 10x = 40

b = 21x = 84

∴ Area of rectangle = lb

⇒ 40 × 84

∴ Area of rectangle = 3360 sq. cm.