Question

A wall, rectangular in shape, has a perimeter of 46 m. If the length of its diagonal is 17 m, what is the area of the wall?
1. 224 m²
2. 120 m2
3. 240 m2
4. 606 m2

Answer 1

Correct Answer - Option 2 : 120 m2

Given:

Perimeter of wall = 46 m

Length of its diagonal is 17 m

Formula Used:

Perimeter of rectangle = 2 (l + b)

(Diagonal)² = (l)² + (b)²

Calculation:

Now,

46 = 2 (l + b)

⇒ l + b = 23

(Diagonal)² = (l)² + (b)²

(17)² = l² + b²

⇒ 289 = l² + b²

(l + b)² = l² + b² + 2lb

⇒ 23² = 289 + 2lb

⇒ lb = (529 - 289)/2 = 120 m²

∴ Area of rectangle = 120 m²