Question

gebra 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
1 define a variable
let w = width
let 2w - 3 = length
less than
is
2 setup equation & solve
translate into an equation using using your let statements. then solve.
what math operation words are in the problem?
p = 2l + 2w
p = 18
18 = 2(2w - 3)+2w
18 = 4w - 6+2w
18 = 6w - 6
+6 +6
24 = 6w
6 6
4 = w
w = 4 cm
3 define answer
give exactly what the problem is asking for.
w = 4 cm
multiple - choice question
what is the length?
length = 11 cm
length = 2 cm
length = 5 cm
length = 14 cm
rewatch

Explanation:

Step1: Set up variables

Let $w$ be the width. Then length $l = 2w - 3$.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2l + 2w$. Given $P = 18$, we substitute $l$: $18=2(2w - 3)+2w$.

Step3: Expand and simplify

$18 = 4w-6 + 2w$, which simplifies to $18=6w - 6$.

Step4: Solve for $w$

Add 6 to both sides: $18 + 6=6w$, so $24 = 6w$. Then $w = 4$ cm.

Step5: Find the length

Substitute $w = 4$ into the length formula $l=2w - 3$. So $l=2\times4 - 3=8 - 3 = 5$ cm.

Answer:

C. Length = 5 cm