Question

The cost of fencing of a rectangular park at Rs. 70/m is Rs. 6,300. If the area of the rectangle is 500 m². Find the breadth of the rectangle is how much percent of the length of the rectangle. (If, Length > Breadth)
1. 40%
2. 50%
3. 80%
4. 75%

Answer 1

Correct Answer - Option 3 : 80%

Given:

Cost of fencing of rectangular park = 6300

Rate of fencing = Rs. 70 / m

Area of rectangle = 500 m²

Formula used:

Perimeter of rectangle = 2 (l + b), where l = length and b = breadth of rectangle

Area of rectangle = l × b = lb

(a – b)² = (a + b)² - 4ab

Let, perimeter of rectangle = X m

∴ 70 × X = 6300

∴ X = 6300 / 70 = 90

X = 2 (l + b)

∴ 2 (l + b) = 90

∴ (l + b) = 45     ---- (1)

⇒ l × b = 500     ---- (2)

⇒ (l – b)² = (l + b)² – 4lb

⇒ (l – b)² = (45)² – 4 × 500

⇒ (l – b)² = 2025 – 2000 = 25

⇒ (l – b) = √25 = 5     ---- (3)

On equating eqn. (1) and (3)

l = 25 and b = 20

⇒ 20 / 25 × 100 = 80%

Therefore, breadth is 80% of length of rectangle