Question

part 1 of 5
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. then translate the statement into an inequality
the perimeter of the rectangle is less than or equal to 70
x + 30 +
70

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $l$ is length and $w$ is width. Here $l = 30$ and let $w=x$. So $P=2(30 + x)=x + 30+x + 30$.

Step2: Set up the inequality

Since the perimeter is no greater than 70, we have $x + 30+x + 30\leq70$.

Step3: Simplify the inequality

Combining like - terms gives $2x+60\leq70$.

Step4: Solve for x

Subtract 60 from both sides: $2x\leq70 - 60$, so $2x\leq10$. Then divide both sides by 2: $x\leq5$.

Answer:

The maximum width of the rectangle is 5 centimeters.