Question

algebra to solve word problems w/ perimeter - google slides
example 2
the length of a rectangle is three centimeters less than twice its width. if the perimeter of the rectangle is 18 centimeters, find its dimensions.
draw a rectangle
l = 2w - 3
define a variable
let w = width
let 2w - 3 = length
what math operation words are in the problem?
p = 2l + 2w
p = 18
multiple - choice question
the equation for the problem is:
18=(2w - 3)+w
18 = 2(2w - 3)+2w
18 = 2(2w - 3 + 2w)
18=(2w - 3)+2w

Explanation:

Step1: Define variables

Let \(w\) be the width of the rectangle. Then the length \(L = 2w-3\) according to the problem description.

Step2: Recall perimeter formula

The perimeter formula of a rectangle is \(P = 2L+2W\). Here \(P = 18\), \(L=2w - 3\) and \(W = w\).

Step3: Substitute values into formula

Substitute \(L\) and \(W\) into the perimeter formula: \(18=2(2w - 3)+2w\).

Answer:

18 = 2(2w - 3) + 2w