Question

the perimeter of a rectangle is to be no greater than 100 centimeters and the length must be 45 centimeters. find the maximum width of the rectangle. first, understand the problem. then translate the statement into an inequality. the perimeter of the rectangle is less than or equal to 100 x + 45 + ≤ 100

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is length and $w$ is width. Here $l = 45$ and $w=x$, so $P=2(45 + x)=90 + 2x$.

Step2: Set up the inequality

Since the perimeter is no greater than 100, we have the inequality $90+2x\leq100$.

Step3: Solve the inequality for $x$

Subtract 90 from both sides: $2x\leq100 - 90$, so $2x\leq10$. Then divide both sides by 2: $x\leq5$.

Answer:

5 centimeters