SOLUTION: Two times the length plus two times the width equals the perimeter of a rectangle. The perimeter of the rectangle is 56 meters. Twice the length of the rectangle is one more than t
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Question 338568: Two times the length plus two times the width equals the perimeter of a rectangle. The perimeter of the rectangle is 56 meters. Twice the length of the rectangle is one more than three times the width. What is the length of the rectangle? What is the width of the rectangle? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Write an equation for each statement:
:
Two times the length plus two times the width equals the perimeter of a rectangle.
2L + 2W = P
:
The perimeter of the rectangle is 56 meters.
2L + 2W = 56
:
Twice the length of the rectangle is one more than three times the width.
2L = 3W + 1
:
Looking at this we can replace 2L in the 2nd equation with (3W+1), so we have:
(3W+1) + 2W = 56
5W + 1 = 56
5W = 56 - 1
5W = 55
W =
W = 11 m is the width
then
we know 2L = 3W + 1; replace W with 11
2L = 3(11) + 1
2L = 33 + 1
L =
L = 17 m is the length
:
;
Check this in the perimeter equation
2(17) + 2(11) = 56
34 + 22 = 56
and
2L = 3W + 1
34 = 3(11) + 1; confirms our solution: L = 17; W = 11
