Question

the perimeter of a rectangle is to be no greater than 70 centimeters and the length must be 30 centimeters. find the maximum width of the rectangle. first, understand the problem. translate the statement into an inequality. the perimeter of the rectangle is to be no greater than 70 centimeters or x + 30+5≤70

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is length and $w$ is width. Here $l = 30$ and $P\leq70$, so $2(30 + w)\leq70$.

Step2: Simplify the inequality

First, distribute the 2: $60+2w\leq70$. Then subtract 60 from both sides: $2w\leq70 - 60$, so $2w\leq10$.

Step3: Solve for width

Divide both sides of the inequality $2w\leq10$ by 2: $w\leq5$.

Answer:

The maximum width of the rectangle is 5 centimeters.