Question 664794: Please help: a rectangle has a length that is 6 inches LESS than 5 times the width. The perimeter of the rectangle is 8 inches MORE than twice the length. Write equation and find dimensions of the rectangle.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! a rectangle has a length that is 6 inches LESS than 5 times the width.
The perimeter of the rectangle is 8 inches MORE than twice the length.
Write equation and find dimensions of the rectangle.
:
Write an equation for each statement
"a rectangle has a length that is 6 inches LESS than 5 times the width."
L = 5W - 6
:
" The perimeter of the rectangle is 8 inches MORE than twice the length."
P = 2L + 8
Replace L with (5W-6) from the 1st equation
P = 2(5W-6) + 8
P = 10W - 12 + 8
P = 10W - 4
:
We know:
2L + 2W = P
Replace L with (5W-6), replace P with (10W-4), find W
2(5W-6) + 2W = 10W-4
10W - 12 + 2W = 10W - 4
Combine like terms
10W - 10W + 2W = -4 + 12
2W = 8
W = 4 inches is the Width
then
L = 5(4) - 6
L = 20 - 6
L = 14 inches is the length
:
Check by finding the perimeter
2(14) + 2(4) = 36
Find 2L + 8, given as the perimeter
2(14) + 8 = 32; confirms our solution
;
Rectangle is 14 by 4
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