SOLUTION: The lenght of a rectangle is 4cm more than its width and 4cm less than the length of a diagonal of the rectangle. What is the area of the rectangle?

Question 173274: The lenght of a rectangle is 4cm more than its width and 4cm less than the length of a diagonal of the rectangle. What is the area of the rectangle?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The length of a rectangle is 4cm more than its width and 4cm less than the length of a diagonal of the rectangle. What is the area of the rectangle?
;
Keep in mind the right triangle formula a^2 + b^2 = c^2
:
Let x = the length of the rectangle (a)
then
(x-4) = width of the rectangle (b)
and
(x+4) = diagonal of the rectangle (c)
:
x^2 + (x-4)^2 = (x+4)^2
FOIL
x^2 + x^2 - 8x + 16 = x^2 + 8x + 16
Combine like terms on the left
x^2 + x^2 - x^2 - 8x - 8x + 16 - 16 = 0
Results
x^2 - 16x = 0
Factor
x(x - 16) = 0
Two solutions;
x = 0
and
x = 16 is the length of the rectangle
then
12 = width of the rectangle
and
20 = diagonal of the rectangle
;
Area = 16 * 12 = 192 sq/cm
:
Check it:
16^2 + 12^2 = 20^2
256 + 144 = 400; confirms our solution for length & width
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