SOLUTION: A rectangle has a perimeter of 78 inches. Its length is 6 inches more than twice its width. a. make a sketch of the rectangle and label its sides b. find the recangle's length

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Question 119405This question is from textbook Mathematics concepts and skills practice workbook
: A rectangle has a perimeter of 78 inches. Its length is 6 inches more than twice its width.
a. make a sketch of the rectangle and label its sides
b. find the recangle's length and width.

I tried doing this but it gets me confused.
I did:
78=2w+6
72=2w
Then I'm just lost. If i continue, the perimeter doesnt add up. Please help!
This question is from textbook Mathematics concepts and skills practice workbook

Found 2 solutions by ankor@dixie-net.com, Earlsdon:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
A rectangle has a perimeter of 78 inches. Its length is 6 inches more than twice its width.
a. make a sketch of the rectangle and label its sides
b. find the recangle's length and width.
I tried doing this but it gets me confused.
I did:
78=2w+6
72=2w
Then I'm just lost. If i continue, the perimeter doesnt add up. Please help!
:
Let's start over:
Let x = width
It said the length is 6" more the twice the width therefore:
(2x+6) = length
:
You know:
2L + 2W = 78
Substitute (2x+6) for L and x for W:
2(2x+6) + 2x = 78
4x + 12 + 2x = 78
6x = 78 - 12
6x = 66
x = 66/6
x = 11" is the width
then
2(11) + 6 = 28" is the length
:
:
Check our perimeter
2(28) + 2(11) =
56 + 22 = 78; confirms our solution
:
:
I think using x in these problems reduces the confusion factor, but you could
use w throughout if you prefer that
,

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Start with the formula for the perimeter of a rectangle:
Substitute:
Simplify.

Substitute
Subtract 12 from both sides.
Divide both sides by 6.
The width is 11 inches.
Substitute

The length is 28 inches.
Check:
Substitute and

OK!