SOLUTION: The are of a rectangle is 400cm^2. If the length of one of its sides is "x"cm, express the length of the other side and hence the perimeter in terms of X. Find the value of X which

Algebra ->  Rectangles -> SOLUTION: The are of a rectangle is 400cm^2. If the length of one of its sides is "x"cm, express the length of the other side and hence the perimeter in terms of X. Find the value of X which      Log On


   

Question 924768: The are of a rectangle is 400cm^2. If the length of one of its sides is "x"cm, express the length of the other side and hence the perimeter in terms of X. Find the value of X which makes the perimeter a minimum.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
...perimeter a minimum?
2x%2B2y=p;
xy=400
If "one of the sides" is x, then the other side is y. LOWER-CASE x; switching case level is incorrect unless you have a specific reason for using both case levels.

y=400%2Fx;
2%28400%2Fx%29%2B2x=p
highlight%28p=800%2Fx%2B2x%29

You want to know for what value of x will p be the minimum.

p=800%2Fx%2B2x%2Ax%2Fx
p=%28800%2B2x%5E2%29%2Fx
This seems not to help. Going back to the red-outlined formula for p, the use of derivative should be useful, since I cannot right now think of a less advanced way.

dp%2Fdx=%28-1%29800x%5E%28-2%29%2B2
dp%2Fdx=2-800%2Fx%5E2
Max or Min?
highlight_green%282-800%2Fx%5E2=0%29
2=800%2Fx%5E2
2%2Ax%5E2=800
x%5E2=400
highlight%28x=20%29

Is this x for a maximum or a minimum?
Letting the technology show us,
graph%28300%2C300%2C-4%2C35%2C-4%2C450%2C800%2Fx%2B2x%29
Indicates that perimeter has a minumum. The value there for the min perimeter should be p=800%2F20%2B2%2A20, p=40%2B40=highlight%2880%29.