Posted by Rachel on Wednesday, May 8, 2013 at 1:02am.
A dog kennel is to be constructed alongside a house using 60 m of fencing. Find the dimensions that will yield the maximum area.
How do you solve this problem?
- algebra 2 - Reiny, Wednesday, May 8, 2013 at 6:56am
I assume you are implying that we don't need a fence along the house.
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
Answer This Question
More Related Questions
- Algebra 2 - A rancher is fencing off a rectangular area with a fixed perimeter ...
- Pre-Algebra-math - Mr.jones bought 20 yards of fencing to make pen for dog pen ...
- Algebra - Suppose you want to enclose a rectangular garden plot against a house ...
- Algebra 2 - One hundred feet of fencing is available to make a rectangular dog ...
- Math - A rectangular dog pen is to be constructed using a barn wall as one side ...
- math - a rectangular pen is to be constructed alongside a barn using 120 feet of...
- MATH 11 help PLease! - A rectangular garden is made at the side of the house. ...
- Adv. Function math - How would you set up this problem if instead of using 1000 ...
- Math - A rectangular livestock pen with THREE SIDES of fencing is to be built ...
- Math - If Steve has 120 feet of fence to make a rectangular kennel and he will ...