SOLUTION: The perimeter of a rectangle is 30 m. If one side is x, express the area of the rectangle in terms of x. Show that there is no value of x such that the area is 60m^2. Thanks

Question 785549: The perimeter of a rectangle is 30 m. If one side is x, express the area of the rectangle in terms of x. Show that there is no value of x such that the area is 60m^2.

Thanks
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= length of one side in meters
= length of the adjacent side in meters
(one is the length of the rectangle, and the other one is the width)
The perimeter (in meters) is
--> -->
The area is

Substituting for , we get
<--> (area expressed in terms of x)
THat is a quadratic function.
It graphs as a parabola, and the vertex is a maximum.
(It is realy a portion of a parabola, because we must only define it for
to have positive numbers for width odf the rectangle.
-->-->-->
The maximum area is found when , and it is .
At that point and the rectangle is a square.
For any other value of , tyhe area is less than that:
, , and
RELATED QUESTIONS
The area of a rectangle is 100m^2. Express the perimeter in terms of x where x is the... (answered by ikleyn)

The area of a rectangle is 100m^2. Express the perimeter in terms of x where s is the... (answered by ikleyn)

The perimeter of a rectangle is 24 feet. a. If x is the measure of one side of the... (answered by josmiceli)

a rectangle has a perimeter 600m. If the rectangle is x meter wide, express the area of... (answered by macston)

The perimeter of a rectangle is 24cm. Express the area of the rectangle in terms of the... (answered by ewatrrr)

The perimeter of a rectangle is 28cm. Express the area of the rectangle in terms of the... (answered by moshiz08)

the perimeter of a rectangle is 32cm. express the area of the rectangle in terms of it's (answered by ramkikk66)

the perimeter of a rectangle is 100 m.Express the area of the rectangle in terms of the... (answered by math_helper)