Question

the perimeter of a rectangle is to be no greater than 80 centimeters and the length must be 25 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 80 x + 25 + ≤ 80

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here $l = 25$ cm and let the width be $x$ cm. So $P=2(25 + x)$.

Step2: Set up the inequality

Since the perimeter is no greater than 80 cm, we have the inequality $2(25 + x)\leq80$.

Step3: Solve the inequality

First, distribute the 2: $50+2x\leq80$. Then subtract 50 from both sides: $2x\leq80 - 50$, so $2x\leq30$. Divide both sides by 2: $x\leq15$.

Answer:

15 cm