# Math

posted by booyah

A rectangular dog pen is to be constructed using a barn wall as one side and 60 meters of fencing for the other three sides. Find the dimensions of the pen that maximize the pen's area.

1. LULU

20 x 20

2. Reiny

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
= x(60-2x)
= -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 )

## Similar Questions

1. ### math

a rectangular pen is to be constructed alongside a barn using 120 feet of fencing. the barn will be used for one side of the pen. What should the dimensions of the pen be to maximize its area. ***Can not use calculus. This is a 9th …
2. ### algebra

Ian wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Ian has 450 feet of fencing, what dimensions would maximize the area of …
3. ### Geometry

A farmer wants to fence in a rectangular pen using the wall of a barn for one side of the pen and 115 feet of fencing for the remaining 3 sides. What dimensions will give her the maximum area for the pen?
4. ### calculus optimization problem

A farmer has 460 feet of fencing with which to enclose a rectangular grazing pen next to a barn. The farmer will use the barn as one side of the pen, and will use the fencing for the other three sides. find the dimension of the pen …
5. ### Math

Manuel wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Manuel has 750 feet of fencing, what dimensions would maximize the …
6. ### math

Trent wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Trent has 400 feet of fencing, what dimensions would maximize the area …
7. ### Math

You are designing a rectangular dog pen off the back of your house. The House will form one side of the dog pen. The pen is to have an area of 800 ft.² but you want to minimize the amount of fencing that you need for the three sides …
8. ### Pre-aljebra

a rectangular dog pen is to be constructed so that one side is against an existing stone wall and the other three sides are to be fenced. of 500 feet of fence is to be used, determine the dimensions and area of the pen with maximum …
9. ### college math

a rectangular dog pen is to be constructed so that one side is against an existing stone wall and the other three sides are to be fenced. of 500 feet of fence is to be used, determine the dimensions and area of the pen with maximum …
10. ### math

a. A rectangular pen is built with one side against a barn. 1200 m of fencing are used for the other three sides of the pen. What dimensions maximize the area of theâ€‹ pen?

More Similar Questions