Question

The numerical values of the area and the perimeter of a square field are in the ratio 5:2, while that of a square park are in the ratio 3:1. What is the positive difference between their areas?

Answer 1

44

Explanation:

If side = a

Then:

• A = a², P = 4a for area and perimeter
• A/P = a²/4a = a/4 for are/perimeter ratio

The first case:

• a/4 = 5/2 ⇒ 2a = 20 ⇒ a = 10 ⇒ a² = 100

The second case:

• a/4 = 3/1 ⇒ a = 12 ⇒ a² = 144

Difference between areas:

• 144 - 100 = 44