SOLUTION: The width of a rectangle is 10 meters less than half of the length. If the perimeter is 52 meters, find the length and the width. I have the answers to this word problem alread

Algebra ->  Rectangles -> SOLUTION: The width of a rectangle is 10 meters less than half of the length. If the perimeter is 52 meters, find the length and the width. I have the answers to this word problem alread      Log On


   

Question 884191: The width of a rectangle is 10 meters less than half of the length. If the perimeter is 52 meters, find the length and the width.
I have the answers to this word problem already, the length=24 and the width=2. What I need is for someone to show me how they got that answer to that problem. Thanks.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Let w = width
Let L = Length

The description's first sentence you can transcribe into w=-10%2BL%2F2.
The second sentence giving perimeter can be set into the formula for the perimeter of a rectangle, 2w%2B2L=52. Sometimes, drawing an rectangle and labeling the parts with the corresponding symbols can help.

Both of those equations use variables L and w. You have a formula for w already, and so you can substitute that expression into the other equation.

2w%2B2L=52
2%28-10%2BL%2F2%29%2B2L=52
L-20%2B2L=52
3L-20=52
3L=52%2B20
3L=72, now divide both sides by 3,
L=24

Now use that to get the value for w.