SOLUTION: A rectangle has a perimeter of 40 cm and a length of x cm. Show that the area A=(20x-x^2)cm^2.

Algebra ->  Equations -> SOLUTION: A rectangle has a perimeter of 40 cm and a length of x cm. Show that the area A=(20x-x^2)cm^2.      Log On


   

Question 1112491: A rectangle has a perimeter of 40 cm and a length of x cm.
Show that the area A=(20x-x^2)cm^2.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Let...
Length = L = x cm (given)
Width = W
Perimeter = P = 40 cm (given)

From properties of rectangles: P = 2L + 2W
Solve this for W:
W = (P-2L) / 2

Also from properties of rectangles:
Area = A = LW
Substitute W=(P-2L)/2 into the equation for A:
A=L*(P-2L)/2

Now substitute the given info:
A = x(40-2x)/2
A = +%2840x+-+2x%5E2%29+%2F+2+
A = +%2820x-x%5E2%29+ +cm%5E2+