Question

using algebra to solve word problems w/ perimeter - google slides
charleno muro
using algebra to solve word problems w/ perimeter - google slides
adrienne
example 1
the length of a rectangle is six inches more than its width. if the perimeter of the rectangle is 24 inches, find its dimensions.
draw a rectangle
w
l = w + 6
define a variable
let w = width
let w + 6 = length
more than
is
help solve & solve
translate into an equation using your let statements. then solve!
what math operation words are in the problem?
p = 2l + 2w
p = 24
24 = 2(w + 6)+2w
24 = 2w + 12+2w
24 = 4w + 12
multiple - choice question
what is the answer to the equation?
w = 12
w = 3
w = 9
w = 4
rewatch

Explanation:

Step1: Set up the perimeter formula

Let the width of the rectangle be \(w\), then the length \(L=w + 6\). The perimeter formula for a rectangle is \(P = 2L+2W\). Substituting \(L\) and \(P = 24\) into the formula, we get \(24=2(w + 6)+2w\).

Step2: Expand the equation

Expand \(2(w + 6)\) to get \(2w+12\). So the equation becomes \(24=2w + 12+2w\).

Step3: Combine like - terms

Combine the \(w\) terms: \(2w+2w = 4w\). The equation is now \(24=4w + 12\).

Step4: Solve for \(w\)

Subtract 12 from both sides: \(24-12=4w+12 - 12\), which simplifies to \(12 = 4w\). Then divide both sides by 4: \(\frac{12}{4}=w\), so \(w = 3\).

Answer:

w = 3