Question

the perimeter of a rectangle is 30 m. the length of the rectangle is 3 m less than twice the width. find the length and width of the rectangle. length m width m

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $P$ is perimeter, $l$ is length and $w$ is width. Given $P=30$, and $l = 2w - 3$. Substitute these into the formula: $30=2((2w - 3)+w)$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $30 = 2(2w-3 + w)=2(3w - 3)$. Then distribute the 2: $30=6w-6$.

Step3: Solve for $w$

Add 6 to both sides of the equation: $30 + 6=6w-6 + 6$, which gives $36 = 6w$. Divide both sides by 6: $w=\frac{36}{6}=6$.

Step4: Solve for $l$

Substitute $w = 6$ into the length - formula $l=2w - 3$. So $l=2\times6-3=12 - 3=9$.

Answer:

length: 9 m
width: 6 m