SOLUTION: A square has an area of 256 cm^2. If the same amount is removed from one dimension and added to the other, the resulting rectangle has an area 16 cm^2 less. Find the dimensions of

Algebra ->  Surface-area -> SOLUTION: A square has an area of 256 cm^2. If the same amount is removed from one dimension and added to the other, the resulting rectangle has an area 16 cm^2 less. Find the dimensions of       Log On


   

Question 932584: A square has an area of 256 cm^2. If the same amount is removed from one dimension and added to the other, the resulting rectangle has an area 16 cm^2 less. Find the dimensions of the rectangle.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
area of a square is 256cm%5E2
Let's represent each side as "x".
Let's represent the amount added and subtracted as "y".
if amount is removed from one dimension and added to the other, one side of rectangle will be:x-y and other side will be x%2By
then the measure of the side of square is sqrt%28256cm%5E2%29=+16cm , or the square is 16cm by 16cm


The equation that can be set up is:
the area of a square is A=x%5E2=256cm%5E2
the area of a rectangle is A%5Br%5D=%28x-y%29%28x%2By%29
since the resulting rectangle has an area 16cm%5E2 less, we have:
x%5E2-16cm%5E2+=%28x%2By%29%28x-y%29+.........solve for x
x%5E2-16cm%5E2+=x%5E2-y%5E2...............the x%5E2 cancels out leaving us:
-16cm%5E2+=-y%5E2.... divide both sides by -1
16cm%5E2+=y%5E2
y=4cm
so, the length of the rectangle is x%2By=16cm%2B4cm=20cm and
the width of the rectangle is x-y=16cm-4cm=12cm
Therefore we can solve this rectangle size as 20cm by 12cm.
The area comes out to be A%5Br%5D=20cm%2A12cm=240cm%5E2