A rectangle has an area of (a^2+4a+4) square inches, and you know that the width is (a+2) inches. You can use long division to determine the length of the box. area = length * width, length = area/width
I got this as my answer The length is going to be a+2
a+2/a^2+4a+4
is this right ?
Yes, a^2 + 4a + 4 = (a+2)^2, so it is a square.
You don't need to do the long division to see that, but is a good idea to know how to do it.
To determine the length of the rectangle, you can indeed use long division using the formula length = area/width. Let's go through the long division process.
Dividing (a^2 + 4a + 4) by (a + 2) using long division:
_________
a + 2 │ a^2 + 4a + 4
- (a^2 + 2a)
____________
2a + 4
- (2a + 4)
__________
0
As you can see, the division is exact, and there is no remainder. This means that (a + 2) completely divides into (a^2 + 4a + 4). Therefore, your answer is correct:
length = a + 2.