What are the dimensions of a rectangle whose length is 4 more than twice the width and whose perimeter is less than 7 times the width?
Please help me out with this question as I've forgotten how to set it up. Thank you.
Let width be W
Then length or L = 2W + 4
Perimeter = 2(L + W), or 2L + 2W, or 2(2W + 4) + 2W, or 4W + 8 + 2W, or 6W + 8
We then get:
6W - 7W + 8 < 0 ------- Subtracting 7W from each side
- W + 8 < 0
- W < - 8 ------ Subtracting 8
Width, or , or
L = 2(9) + 4 ------ Substitute 9 for W
L = 18 + 4, or
If you substitute a different value for W: the width - one that's greater than 8 - the length's value will change.