SOLUTION: the length of a rectangle is twice as long as its width. Express the area of the rectangle as a function of its perimeter
Algebra.Com
Question 273321: the length of a rectangle is twice as long as its width. Express the area of the rectangle as a function of its perimeter
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The first thing we know is that 
The next thing we know is that the perimeter of a rectangle is given by:
Substituting we discover that:
or
The area of a rectangle is given by:
Substituting:
\ =\ \left(\frac{P}{3}\right)\left(\frac{P}{6}\right)\ =\ \frac{P^2}{18})
Check the answer for reasonability:
Consider a 2' by 4' rectangle.
The area is 8 ft². The perimeter is 2 times 4 plus 2 times 2 equals 8 plus 4 equals 12'
\ =\ \frac{12^2}{18}\ =\ \frac{144}{18}\ =\ 8)
Seems to work.
John
RELATED QUESTIONS
express the perimeter P of a rectangle as a function of the width w if the length of the... (answered by user_dude2008,Fombitz)
express the perimeter P of the rectangle as a function of the Length L if the width of... (answered by rfadrogane)
Express the area, A, of a rectangle as a function of the width, W, if the width of the... (answered by ikleyn)
Express the area A of a rectangle as a function of the length x if the length of the... (answered by nyc_function)
The perimeter of a rectangle 28.8 centimeters. The length of the rectangle is twice as... (answered by nyc_function)
a rectangle has area 40m square. Express the perimeter of the rectangle as a function of... (answered by Math_Boss)
Express the perimeter p of a rectange as a function of the Length L if the length of the... (answered by stanbon)
A rectangle has one side twice the length of the other. Express the area of the... (answered by vleith)
The area (A) of a rectangle is length (l) times its width (w). Express the area of the... (answered by MathLover1)