Question

using algebra to solve word problems w/ perimeter - google slides
adrienne
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
setup equation & solve
what math operation words are in the problem?
p = 2l + 2w
p = 18
18 = 2(2w - 3)+2w
define a variable
let: w = width
let: 2w - 3 = length
less than
is
multiple - choice question
what is the first step in solving the equation
subtract 2w from both sides.
divide both sides of the equation by 2.
distribute (open the parentheses).
combine like terms.
rewatch

Explanation:

Step1: Recall the perimeter formula

The perimeter of a rectangle is \(P = 2L+2W\).

Step2: Define variables

Let \(w\) be the width and \(L = 2w - 3\) be the length.

Step3: Substitute into the formula

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

Step4: Identify the first - solving step

To solve \(18=2(2w - 3)+2w\), the first step is to distribute the 2 in \(2(2w - 3)\) according to the distributive property \(a(b + c)=ab+ac\). So we get \(18 = 4w-6 + 2w\).

Answer:

Let \(w\) be the width of the rectangle. The length \(L = 2w - 3\). The perimeter formula is \(P=2L + 2W\), and \(P = 18\). Substituting \(L\) into the perimeter formula gives \(18=2(2w - 3)+2w\). The first - step in solving this equation is to distribute (open the parentheses). So the answer is: Distribute (open the parentheses).