SOLUTION: The area of a rectangle is 21 cm square. If one side exceeds the other by 4 cm, Find the dimensions of the rectangle.

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Question 1199532: The area of a rectangle is 21 cm square. If one side exceeds the other by 4 cm, Find the dimensions of the rectangle.
Answer by math_tutor2020(3817) About Me  (Show Source):
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Answer: 3 cm by 7 cm rectangle
3*7 = 21

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Explanation:

Let's list the ways to factor 21 with positive values:
1*21 = 21
3*7 = 21

The gap from 3 to 7 is 4 units, because 7-3 = 4, so it's fairly clear that we have a 3 by 7 rectangle.

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Another approach using algebra.

x = width
x+4 = length which is four units larger than the width

area = length*width
area = (x+4)*x
area = x^2+4x

We'll set this equal to the stated area 21 square cm, and solve for x.

x^2+4x = 21
x^2+4x-21 = 0

From here you can factor like so
x^2+4x-21 = 0
(x-3)(x+7) = 0
x-3 = 0 or x+7 = 0
x = 3 or x = -7
Ignore x = -7 because it makes no sense to have a negative length or width.

If x = 3, then x+4 = 3+4 = 7
We arrive at 3*7 = 21 to confirm the answers.

Another way to solve x^2+4x-21 = 0 is to use the quadratic formula.
We have
a = 1
b = 4
c = -21
to get the following steps:
x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-4%2B-sqrt%28%284%29%5E2-4%281%29%28-21%29%29%29%2F%282%281%29%29

x+=+%28-4%2B-sqrt%28100%29%29%2F%282%29

x+=+%28-4%2B-++10%29%2F%282%29

x+=+%28-4%2B10%29%2F%282%29 or x+=+%28-4-10%29%2F%282%29

x+=+%286%29%2F%282%29 or x+=+%28-14%29%2F%282%29

x+=+3 or x+=+-7
Then as mentioned earlier, we ignore the negative x value and have x = 3 lead to x+4 = 7.