Question

the perimeter of a rectangle is to be no greater than 100 centimeters and the width must be 5 centimeters. find the maximum length of the rectangle. (type an integer.) the maximum length of the rectangle is

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $w = 5$ cm and $P\leq100$ cm.

Step2: Substitute values into the perimeter formula

Substitute $w = 5$ into $P = 2(l + w)$: $P=2(l + 5)$. Since $P\leq100$, we have the inequality $2(l + 5)\leq100$.

Step3: Solve the inequality for $l$

First, divide both sides of the inequality $2(l + 5)\leq100$ by 2: $l + 5\leq50$. Then subtract 5 from both sides: $l\leq45$.

Answer:

45