Question

The area of a triangular field whose sides are 65 m 72 m, and 97 m is equal to the area of a rectangular park whose sides are in the ratio of 5 ∶ 13. What is the perimeter (in m ) of the rectangular park?
1. 144
2. 180
3. 108
4. 216

Answer 1

Correct Answer - Option 4 : 216

Given:

Length of triangle = 97 m

Base of a triangle =65 m

Height of triangle = 72 m

Ratio of length and breadth of a rectangle = 5 : 13

Formula used:

Area of triangle = 1/2 × base × height 

Area of rectangle = length × breadth

Perimeter of rectangle = 2(l + b)

Calculation:

Let the ratio of length and breadth of rectangle be 5x and 13x

According to the question

⇒ (1/2 × 65 × 72) = (5x × 13x)

⇒ (65 × 36) = 65x²

⇒ x² = (65 × 36)/65

⇒ x² = 36

⇒ x = 6 m

Perimeter of rectangle = 2(5x + 13x)

⇒ (2 × 18x)

⇒ 36x

Now,

⇒ (36 × 6) = 216 m

∴ Perimeter of rectangle is 216 m