SOLUTION: Start with a square. Double its base, then shrink its height by 3inch. The new rectangle's area is 40 square inches loarger than the area of the original square. How long are the s

Algebra ->  Rectangles -> SOLUTION: Start with a square. Double its base, then shrink its height by 3inch. The new rectangle's area is 40 square inches loarger than the area of the original square. How long are the s      Log On


   

Question 1740: Start with a square. Double its base, then shrink its height by 3inch. The new rectangle's area is 40 square inches loarger than the area of the original square. How long are the sides of the square?
Answer by xen0gears(3) About Me  (Show Source):
You can put this solution on YOUR website!
(Please ignore all dotted lines [---] in the pictures. They are there so the picture would come out right.)
Suppose your original square has side length x:
_____
|-------|
|-------| x
|_____|
x (not to scale)
Then its area is +x%5E2+. Doubling the base gives the following shape:
__________
|-------------|
|-------------| x
|__________|
2x (not to scale)

Shrinking the height by 3 inches gives the following shape:

__________
|-------------| x-3
|__________|
2x (not to scale)

The area of this new rectangle is +2%2Ax%2A%28x-3%29+=+2x%5E2+-+6x+.
This area is 40 square inches larger than the area of the original square.
Recall that the area of the original square is +x%5E2+.
This gives us the equation +x%5E2+%2B+40+=+2x%5E2+-+6x+.
Subtracting +x%5E2+ from both sides gives +40+=+x%5E2+-+6x+.
Then we subtract 40 from both sides to get +0+=+x%5E2+-+6x+-+40+.
We can factor this into +0+=+%28x-10%29%2A%28x%2B4%29+, which means x = 10 or
x = -4.
Since x represents the length of the side of a square, x cannot be less than zero. Hence, x = 10 inches.