Question

1. parallelogram pqrs is a square. the length of side pq = 2x + 8 and the perimeter of pqrs = 96. what is the length of side pq?

Explanation:

Step1: Set up perimeter equation

A square has 4 equal sides, so perimeter $P = 4 \times \text{side length}$. Substitute the given values:
$$96 = 4(2x + 8)$$

Step2: Solve for $x$

First divide both sides by 4:
$$\frac{96}{4} = 2x + 8$$
$$24 = 2x + 8$$
Subtract 8 from both sides:
$$24 - 8 = 2x$$
$$16 = 2x$$
Divide by 2:
$$x = \frac{16}{2} = 8$$

Step3: Calculate length of PQ

Substitute $x=8$ into $2x + 8$:
$$PQ = 2(8) + 8$$

Answer:

24