SOLUTION: The perimeter of a rectangle is 74 cm. The length of the rectangle is 5 cm less than twice the width. Find the dimensions of the rectangle.

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Question 386806: The perimeter of a rectangle is 74 cm. The length of the rectangle is 5 cm less than twice the width. Find the dimensions of the rectangle.
Answer by gwendolyn(128) About Me  (Show Source):
You can put this solution on YOUR website!
Rectangles have two pairs of sides with exactly the same measure.
Two of the measures are the width
Two of the measures are the length
let W=width
let L=length
The perimeter of a rectangle is the sum of the lengths of all its sides.
Two of these sides are equal to W, and 2 are equal to L. The equation can therefore be represented as:
2W+2L=74
We know that the rectangle's length is 5 less than 2 times its width. This can be expressed as:
L=2W-5
We now have L in terms of W. This can be substituted into our first equation.
2W+2L=74
2W+2(2W-5)=74
2W+4W-10=74
6W-10=74
6W=84
W=14
We have the width of the rectangle. We can substitute this into the second equation to find the length.
L=2W-5
L=2%2A14-5
L=28-5
L=23
So, the length of the rectangle is 23 and the width is 14.
This answer can be checked by plugging both values into the first equation.
2W+2L=74
2%2A14%2B2%2A23=74
28+46=74
74=74
Since 74 is equal to 74, the values we determined for width and length are accurate.