UPSC Prelims 2016·CSAT·Quantitative Aptitude·Geometry and Mensuration

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?

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Last updated 23 May 2026, 3:31 pm IST
  1. A400 sq mCorrect
  2. B300 sq m
  3. C200 sq m
  4. D80 sq m

Explanation

To solve this, we use a fundamental principle of geometry and algebra: for a fixed perimeter, the area of a rectangle is maximized when it is a square. The area of the field is the product of its length and breadth, which is X1 multiplied by X2. We are given that X1 plus X2 equals 40 meters. According to the Arithmetic Mean-Geometric Mean inequality, the product of two numbers with a fixed sum is highest when the numbers are equal. Therefore, the area is maximum when X1 equals X2. If X1 and X2 are equal, then each must be 20 meters because 20 plus 20 equals 40. The maximum area is calculated as 20 meters multiplied by 20 meters, which equals 400 square meters. Since 400 square meters is the maximum possible area, the area will not exceed this value. Thus, Option A is correct.
Quantitative Aptitude: An agricultural field is in the form of a rectangle having length X1 meters and breadth X2 meters (X1 and X2 are variabl
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