Question

the perimeter of a rectangle is to be no greater than 100 centimeters and the length must be 35 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 + 35 + x + 35

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=x + 35$ and $w=x$, so $P=2((x + 35)+x)=2(2x + 35)=4x+70$.

Step2: Set up the inequality

The perimeter is less than or equal to 100. So, we set up the inequality $4x + 70\leqslant100$.

Step3: Solve the inequality

Subtract 70 from both sides: $4x+70 - 70\leqslant100 - 70$, which gives $4x\leqslant30$. Then divide both sides by 4: $x\leqslant\frac{30}{4}=7.5$.

Answer:

The maximum width $x$ is 7.5 centimeters.