QUESTION

CSAT

Hard

Maths

Prelims 2016

An agricultural field is in the form of a rectangle having length X1X1 meters and breadth X2X2 meters (X1X1 and X2X2 are variable). If X1+X2=40X1 + X2 = 40 meters, then the area of the agricultural field will not exceed which one of the following values?

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Explanation

Given: Length of the agricultural field = X1X1 meters Breadth of the agricultural field = X2X2 meters X1+X2=40X1 + X2 = 40 meters The area A of the rectangular field is given by: A=X1X2A = X1 \cdot X2

To find the maximum area: We know that for a rectangle, the area is maximized when the length and breadth are equal. Since X1+X2=40X1 + X2 = 40, the maximum area will occur when: X1=X2=402=20X1 = X2 = \frac{40}{2} = 20 meters

So, the maximum area is: A=X1X2=2020=400A = X1 \cdot X2 = 20 \cdot 20 = 400 sq meters

Therefore, the area will not exceed 400 sq meters.

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