Question

1. the perimeter of a rectangle is at most 24 cm. two opposite sides are both 4 cm long. what are the possible lengths of the other two sides?

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ and $w$ are the length and width. Let the known side be $a = 4$ cm and the unknown side be $x$ cm. So $P=2(4 + x)$.

Step2: Set up inequality

Since the perimeter is at most 24 cm, we have the inequality $2(4 + x)\leq24$.

Step3: Solve the inequality

First, divide both sides of the inequality by 2: $4 + x\leq12$. Then subtract 4 from both sides: $x\leq12 - 4$, so $x\leq8$. Also, the length of a side must be greater than 0. So $0 < x\leq8$.

Answer:

The possible lengths of the other two sides are any real - numbers $x$ such that $0 < x\leq8$ cm.