Question 541356: The length of a rectangle is 3 meters shorter than 3 times its width. Find the length and width if the perimeter is 210 meters. Please help
Answer by ShortCircuit(2)   (Show Source):
You can put this solution on YOUR website! We are going to define length as a variable L and width as a variable W.
You know that length is 3 meters shorter than 3 times it's width, which is like saying L is 3 times W minus 3, or L=3W-3
The equation for perimeter (P) of a rectangle is: P = L + L + W + W
because there are two sides for L and two sides for W
We know that L = 3W-3, so you can plug that into the equation:
P = 3W-3 + 3W -3 + W + W
You know that P = 210, so you can add that into the equation
210 = 3W-3 + 3W -3 + W + W
Now we need to solve for W:
First add all of the width's together and all of the other numbers not attached to variables (separately)
210 = 8W-6
Add 8 to both sides:
216 = 8W
Divide each side by 8:
27 = W
So you know that the width is 27
To find the length, put the value of W back into the equation for length:
L = 3W-3 --> L = 3(27) - 3 --> L = 78
Now you have both the length and width!
Length = 78 meters, Width = 27 meters
To check your answers, you can plug both numbers back into the equation for perimeter:
210 = 78 + 78 + 27 + 27
210 = 210
This is true, so you know you got the correct answer!
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