Question

A rectangular pen is made with 180 meters of fencing on three sides. The fourth side is a stone wall. What is the greatest possible area of such an enclosure?

Answer 1

Let the sides of the pen be ' x ' and ' y ' respectively. for a rectangle you need to sides to be mentioned out of four for its special geometrical structure.

180 meters of fencing includes sum of three sides.

x + 2.y = 180

then express x in terms of y.

x = -2.y + 180

value of the area enclosed

i.e. x.y = 180.y - 2.y^2

then we have to maximise it w.r.t. to y. ( Take derivative w.r.t. y , then equate it to zero.)

Find the value of y , by maximising area and then put the value of x and y in the formula for area.
This is the required answer.

But you must do it further.