Question

look at this parallelogram. find the value of p.
image of a purple parallelogram with top side labeled p and right side labeled 9.1 cm
perimeter = 49.6 centimeters
p = □ centimeters

Explanation:

Step1: Recall the perimeter formula for a parallelogram

The perimeter \( P \) of a parallelogram is given by \( P = 2(a + b) \), where \( a \) and \( b \) are the lengths of adjacent sides. Here, one side is \( p \) and the other is \( 9.1 \) cm, and the perimeter is \( 49.6 \) cm. So we have the equation \( 49.6 = 2(p + 9.1) \).

Step2: Solve for \( p \)

First, divide both sides of the equation by 2: \( \frac{49.6}{2}=p + 9.1 \). Calculating \( \frac{49.6}{2} \), we get \( 24.8=p + 9.1 \). Then, subtract \( 9.1 \) from both sides: \( p=24.8 - 9.1 \).

Step3: Calculate the value of \( p \)

\( 24.8-9.1 = 15.7 \).

Answer:

\( 15.7 \)