Question 839772: Solve algebraically, using one variable. The length of a rectangle is three less than twice the width. If the perimeter is 24 inches, what are the length and width of the rectangle?
Answer by mxgirl22(39)   (Show Source):
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Solve algebraically, using one variable. The length of a rectangle is three less than twice the width. If the perimeter is 24 inches, what are the length and width of the rectangle?
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1.) Get key information out.
length (l) of a rectangle is(=) three (3) less (-) than twice(x2) the width(w).
So length = 2(times)width-3
1ength = 2w-3
width = w
perimeter is(=) 24 inches
perimeter = 24 inches
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2.) Set up your equation.
***Note: Formula for perimeter is: 2 ( l + w )
2 ( l + w ) = 24
2[(2w-3)+(w)] = 24
(4w-6)+(2w) = 24
4w-6+2w = 24
6w-6 = 24
6w-6+6 = 24+6
6w = 30
6w/6 = 30/6
w = 5
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3.) Using the value we got for "w" in step 2, plug in to what we said the length is equal to in step 1. (1 = 2w-3 ).
length= 2w-3
l=2(5)-3
l=10-3
l=7
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4.) Check with perimeter formula. p = 2( l + w )
Use l=7, w=5, p=24
p = 2( l + w )
24= 2[ (7)+(5) ]
24=14+10
24=24
Answers check!
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5.) Answer.
If the perimeter is 24 inches, the length of the rectangle is 7 inches and width is 5 inches.
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