SOLUTION: The plan of a factory building is shown. The length is 25 metres longer than the width. The perimeter of the building is 134 metres. Write an equation and solve it to find the valu
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Question 987425: The plan of a factory building is shown. The length is 25 metres longer than the width. The perimeter of the building is 134 metres. Write an equation and solve it to find the value of x.
Hi that's my question and I was wondering if you could not just tell me the answer but could you explain how you would work it out. My methods I used have just been guessing for these types of questions. I really want to find a more efficient way of answering it. Found 2 solutions by solver91311, macston:Answer by solver91311(24713) (Show Source):
The first thing you have to do is to decide exactly what the variable represents. Until you do that, nothing you do will make any sense. So let's start with the first sentence of every word problem solution you will ever write:
"Let represent..."
For this problem, I would suggest that you let represent the width.
The next thing you need is to represent the length in terms of the width, in this case the variable . The problem says that the length is 25 meters greater than the width. Now what would you say is an expression involving that is 25 larger than ?
Once you have the two expressions in , one to represent the width and one to represent the length, you can consider the formula for the perimeter of a rectangle.
You are given the value of the perimeter, so you can plug that in. We decided that the width is , so you can replace with . And then you can substitute the expression you derived to represent the length in place of . You will end up with a linear equation in that you can solve by ordinary means.
John
My calculator said it, I believe it, that settles it
You can put this solution on YOUR website! .
I don't know what x is, but:
.
W=width; L=length=W+25m; P=perimeter=134m
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P=2(L+W) Put in value for P
134m=2(L+W) Divide each side by 2.
67m=L+W Substitute for L.
67m=(W+25m)+W Subtract 25m from each side.
42m=2W Divide each side by 2.
21m=W
ANSWER 1: The width is 21 meters.
.
L=W+25m=21m+25m=46m
ANSWER 2: The length is 46 meters.
.
CHECK:
P=2(L+W)
134m=2(46m+21m)
134m=2(67m)
134m=134m
