Question

The perimeter of a rectangle is 82 m and its area is 400 m². The breadth of the rectangle is ______.

विकल्प

• 25 m

• 20 m

• 16 m

• 9 m

Answer 1

The perimeter of a rectangle is 82 m and its area is 400 m². The breadth of the rectangle is 16 m.

Explanation:

Let the length and breadth of the rectangle be `l` and b.

Perimeter of the rectangle = 82 m 

⇒ `2 xx (l + b) = 82` 

⇒ `l + b = 41` 

⇒ `l = (41 - b)`   ...(i) 

Area of the rectangle = 400 m² 

⇒ `l xx b = 400  m^2` 

⇒ (41 – b)b = 400   ...(Using (i)) 

⇒ 41b – b² = 400 

⇒ b² – 41b + 400 = 0 

⇒ b² – 25b – 16b + 400 = 0 

⇒ b(b – 25) – 16(b – 25) = 0 

⇒ (b – 25) (b – 16) = 0 

⇒ b = 25 or b = 16 

If b = 25, we have

`l` = 41 – 25

`l` = 16 

Since, `l` cannot be less than b, 

∴ b = 16 m