SOLUTION: The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. Wh
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Question 194145: The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What is the width?
P = 2l + 2w
160 = (2l + 4) +(2w +7) When I substitute, it is just a mess.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let P = perimeter, L=length, and W=width
Note: the lower case letter "l" looks very similar to the number 1. So I'm using an uppercase L. So I figured to use uppercase for all the variables.
Now let's get the translations down:
"The perimeter of a rectangle is six times the width" translates to
Also, "If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches" translates to
Finally, this is not explicitly stated, but the formula for the perimeter of any rectangle is
Start with the given perimeter formula
Plug in
Subtract 2W from both sides
Combine like terms.
Rearrange the equation
Divide both sides by 2 to isolate L
Reduce
-----------------------------------------------
Move onto the second equation
Distribute
Combine like terms.
Plug in
Multiply
Combine like terms.
Subtract 22 from both sides.
Combine like terms.
Divide both sides by 6 to isolate W
Reduce
So the width is
Go back to the previously isolated formula
Plug in
Multiply
So the length is
-----------------------------------------------------------
Answer:
So the width is 23 inches and the length is 46 inches.
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