Question

the perimeter of a rectangle is to be no greater than 170 centimeters and the length must be 50 centimeters. find the maximum width of the rectangle. first, understand the problem. the perimeter of the rectangle is or state the statement into an inequality.

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is given by $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l = 50$ and $w=x$. So $P=2(50 + x)$.

Step2: Set up the inequality

We know that the perimeter $P\leq170$. Substituting $P = 2(50 + x)$ into the inequality, we get $2(50 + x)\leq170$.

Step3: Solve the inequality for $x$

First, distribute the 2: $100+2x\leq170$. Then subtract 100 from both sides: $2x\leq170 - 100$, so $2x\leq70$. Divide both sides by 2: $x\leq35$.

Answer:

The maximum width of the rectangle is 35 centimeters.