Question

the perimeter of a rectangle is 52 m. the length is 2 m more than three times the width. find the length and the width of the rectangle. the width of the rectangle is and the length of the rectangle is

Explanation:

Step1: Set up the perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $P$ is the perimeter, $l$ is the length and $w$ is the width. Given that $P=52$ m and $l = 3w + 2$. Substitute these into the formula: $52=2((3w + 2)+w)$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $52 = 2(4w + 2)$. Then distribute the 2: $52=8w + 4$.

Step3: Solve for the width $w$

Subtract 4 from both sides of the equation: $52−4=8w$, so $48 = 8w$. Divide both sides by 8: $w=\frac{48}{8}=6$ m.

Step4: Solve for the length $l$

Substitute $w = 6$ into the length - width relationship $l=3w + 2$. Then $l=3\times6+2=18 + 2=20$ m.

Answer:

The width of the rectangle is 6 m and the length of the rectangle is 20 m.