20 x 20
let the length be y m (the single side)
let the width be x m
so we know that 2x + y = 60
or y = 60 - 2x
Area = xy
= -2x^2 + 60x
At this point I don't if you know Calculus or not.
If you do, then
d(Area)/dx = -4x + 60
= 0 for a max of area
-4x + 60 = 0
x = 15
then y = 30
if you don't take Calculus, we have to complete the square
area = -2(x^2 - 30x)
= -2(x^2 - 30x + 225 - 225)
= -2((x-15)^2 - 225)
= -2(x-15)^2 + 450
so the area is a maximum when x = 15
and then y = 60-30 = 30
by either method,
the width has to be 15 m, and the length has to be 30 m for a maximum area of 15(30) or 450 m^2
(LULU's answer only gives an area of 400 )
Answer this Question
algebra - Ian wants to build a rectangular pen for his animals. One side of the ...
math - a rectangular pen is to be constructed alongside a barn using 120 feet of...
Math - Manuel wants to build a rectangular pen for his animals. One side of the ...
Geometry - A farmer wants to fence in a rectangular pen using the wall of a barn...
calculus optimization problem - A farmer has 460 feet of fencing with which to ...
geometry - Polly decides to use a wall of the house as one sideof the ...
precalc - Old McDonald has 1000 feet of fencing, and wants to build a pen along ...
math - a farmer has enough fencing to build 40 feet of fence. He wishes to build...
calculus - a farmer wants to make a rectangular pen from 200 feet of fencing. he...
math - A rectangular animal pen will be built using 200 meters of fencing. If ...