Problema Solution
You have 25 meters of fencing and wish to enclose a rectangular pen for a couple of animals that has an area of 63 square meters. Additionally, one side of the pen will be an existing stone wall, so you only have to provide fencing for three sides of the rectangle. what should the dimensions be?
Answer provided by our tutors
let
l = the length of the rectangular pen, l>0
w = the width of the rectangular pen, w>0
l >= w
You have 25 meters of fencing and one side of the pen will be an existing stone wall
l + 2w = 25
l = 25 - 2w
the area is 63 square meters
l*w = 63
plug l = 25 - 2w into the last equation
(25 - 2w)*w = 63
by solving we find
w1 = 3.5 m
w2 = 9 m
click here to see the step by step solution of the equation
l1 = 25 - 2*3.5
l1 = 18 m
l2 = 25 - 2*9
l2 = 7 m but since l>=w follows the solution is l = 18 m and w = 9 m.
the dimensions are: the length is 18 meters and the width is 9 meters.