SOLUTION: Please help me with this problem I'm sure there's a simple solution to solving it, but my book only provides the answer, not the actual explanation of how to solve it. First, th

Question 69613This question is from textbook The Best Test Preperation for the ELM
: Please help me with this problem I'm sure there's a simple solution to solving it, but my book only provides the answer, not the actual explanation of how to solve it.
First, the question is, find the perimeter of rectangle PQRS.
The top length side of the rectangle (PQ) is 11 inches.
The bottom length side (SR) is (7x-3) inches.
The right width side (QR) is (3x-3) inches.
The left width side (PS) is unknown.
I have already solved for x with this equation 7x-3=11 which =2, but when I insert 2 into the equation 3x-3 and add all the sides to find the perimeter of the rectangle it doesn't match the answer in the book.

This question is from textbook The Best Test Preperation for the ELM

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
You apparently have done everything correctly so far. If you have written the problem correctly, there is a chance that the book is wrong.
You have correctly identified PQ as 11 units long. Therefore, you correctly said that side SR must also be 11 units long. And since SR equals 7x-3, you correctly set 7x - 3 equal to 11 units and solved this equation to find that x=2 units.
You did not explain much further, but QR is given as 3x-3. Since you now know that x=2, you can substitute to find that:

This simplifies to:

and this tells you that QR = 3
But the opposite sides of a rectangle are equal in length. Since side PS is opposite to side QR, its length must also be 3.
In summary you have PQ = 11, QR = 3, SR = 11, and PS = 3. If you add these four lengths you find that the perimeter is 28 units long.
If this doesn't agree with the book answer, you either provided some wrong information on the problem or the book answer is wrong. Go through the above work and see if it tracks exactly with the problem information from the book. If it does, then the publisher of the book made an error. [Believe me, it wouldn't be the first time a publisher made a mistake.]