The length of a rectangular field is 23 m more than its breadth. If the perimeter of the field is 206m, then its area is

Question

Philoid · Accepted Answer

Given: Length of field (l) = 23 + breadth(b) = 23 + b

Perimeter of field = 206 m

We know that,

Perimeter = 2(l + b)

⇒ 206 = 2(23 + b + b)

⇒ 206 = 2(23 + 2b)

⇒ 206 = 46 + 4b

⇒ 4b = 206 – 46

⇒ 4b = 160

⇒ b = 40 m

Therefore,

Length of field = 23 + b

= 23 + 40

= 63 m

Now,

Area of rectangle = Length × Breadth

= 63 × 40

= 2520 m²