SOLUTION: How do I work this equation? 2. Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm. a) Set up an e

Question 315712: How do I work this equation?
2. Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm.
a) Set up an equation for the perimeter involving only W, the width of the rectangle.
Answer:
b) Solve this equation algebraically to find the length of the rectangle. Find the width as well.
Answer: Length ______, Width ______

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
The length, L, can be expressed in terms of the width, W, thus:
1) L = 2W+3 "...the length ...is 3cm longer than twice the width..."
The perimeter of a rectangle is given by:
2) P = 2L+2W
a) Substitute equation 1) for L in equation 2)
2(2W+3)+2W = P Simplify.
4W+6+2W = P
6W+6 = P or
b) Substitute P = 90 and solve for W.
6W+6 = 90 Subtract 6 from both sides.
6W = 84 Divide both sides by 6.
W = 14 and...
L = 2W+3
L = 2(14)+3
L = 31
Length = 31cm.
Width = 14cm.
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