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Question 904655: The length of Antonio's rectangular room is 12 feet longer than its width. The area of the room's floor is 448 square feet. What are the dimensions of the room?
Answer by AlgebraLady88(44)   (Show Source):
You can put this solution on YOUR website! We will give the width of the room the variable , w.
We are told the length of the room is 12 feet longer than the width of the room. Therefore, the length of the room is w +12
The area of the room is 448 square feet.
So, we know that length times width will give us the area of the room and can then write out the equation below:
w * (w + 12) = 448
w^2 + 12w = 448
w^2 + 12w - 448 = 0
We now have a quadratic equation .
We know that 448 = 112 * 4 = 28 * 4 * 4 = 28 * 16
We can now factor the quadratic equation above.
( w + 28)( w- 16) = 0
W + 28 =0
w = -28
or w -16 =0
w = 16
We will use the value 16 as the length cannot be a negative number.
Now we see that the width is 16 feet and the length would be 28 feet, which is 12 feet longer than the width.
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