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?
1 Answer
Dec 31, 2015
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.
