Question

the length of a rectangle is 3 more than triple the width. if the perimeter of the rectangle is 118, find the width and length of the rectangle.

1. what is the length of the rectangle?

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$. Then the length $l = 3w + 3$.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Given $P = 118$, we substitute $l$ and $P$ into the formula: $118=2((3w + 3)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $118=2(4w + 3)$. Then distribute the 2: $118 = 8w+6$.

Step4: Solve for $w$

Subtract 6 from both sides: $118 - 6=8w$, so $112 = 8w$. Divide both sides by 8: $w=\frac{112}{8}=14$.

Step5: Solve for $l$

Substitute $w = 14$ into the length formula $l = 3w+3$. Then $l=3\times14 + 3=42 + 3=45$.

Answer:

The width of the rectangle is 14 and the length is 45.