Question

An agricultural field is in the form of a rectangle having length X₁ meters and breadth X₂ meters (X₁ and X₂ are variable). If X₁ + X₂ = 40 meters, then the area of the agricultural field will not exceed  which one of the following values?
(a) 400 sq m 

(b) 300 sq m 

(c) 200 sq m 

(d) 80 sq m

Answer 1

(a) Given, length = x₁m and breadth = x₂m
Also, x₁ + x₂ = 40 where x₁ and x₂ are variables
We know that, of all the rectangles, a square has the largest area.

For the given rectangle to be a square x₁ = x₂

So, x₁ + x₂ = 40 ⇒ x₁ = x₂ = 20 m​

Maximum area of the given rectangle = x₁x₂
= (20 × 20)m² = 400 m²