Question

the perimeter of a rectangle is to be no greater than 80 centimeters and the length must be 35 centimeters. find the maximum width of the rectangle. next, apply the multiplication property of inequality. 2x≤10 x≤5 (simplify your answer.) finally, interpret the result. the maximum width of a rectangle with a perimeter no greater than 80 centimeters and a length of 35 centimeters is centimeters.

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. Given $l = 35$ and $P\leq80$.

Step2: Substitute values into formula

Substitute into $P = 2(l + w)$: $80\geq2(35 + x)$ (let $x$ be the width).

Step3: Solve the inequality

First, divide both sides of the inequality $80\geq2(35 + x)$ by 2: $\frac{80}{2}\geq35 + x$, so $40\geq35 + x$.

Step4: Isolate the variable

Subtract 35 from both sides: $40-35\geq x$, which simplifies to $x\leq5$.

Answer:

5