Question

the perimeter of a rectangle is to be no greater than 110 centimeters and the width must be 25 centimeters. find the maximum length of the rectangle. (type an integer.) the maximum length of the rectangle is

Explanation:

Step1: Recall perimeter formula

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

Step2: Substitute known values

We know that $P\leq110$ and $w = 25$. Substituting into the formula gives $110\geq2(l + 25)$.

Step3: Solve the inequality for $l$

First, divide both sides of the inequality $110\geq2(l + 25)$ by 2: $\frac{110}{2}\geq l + 25$, so $55\geq l+ 25$.
Then subtract 25 from both sides: $l\leq55 - 25$.
So $l\leq30$.

Answer:

30