SOLUTION: The perimeter of a rectangle is 28cm. Express the area of the rectangle in terms of the width x

Algebra ->  Rectangles -> SOLUTION: The perimeter of a rectangle is 28cm. Express the area of the rectangle in terms of the width x      Log On


   

Question 466972: The perimeter of a rectangle is 28cm. Express the area of the rectangle in terms of the width x
Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
Recall that the perimeter is the sum of the lengths of all sides. Also recall that opposite sides of a rectangle have the same length. Therefore
perimeter = width + length + width + length
perimeter = 2 * width + 2 * length
The perimeter is 28 and the width is x, so we have
28 = 2*x + 2*length
Now we can solve for the length in terms of x.
2*length = 28 - 2*x
length = 14 - x
Finally since the area is
Area = length * width
the final expression in terms of x will be
Area = (14-x) * x = 14*x - x^2