Question

look at this parallelogram. find the value of z.
10 cm
perimeter = 30 centimeters
z = \boxed{} centimeters

Explanation:

Step1: Recall parallelogram perimeter formula

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 \( a = 10 \) cm, the other side is \( z \), and \( P = 30 \) cm.

Step2: Substitute values into the formula

Substitute \( P = 30 \) and \( a = 10 \) into \( P = 2(a + z) \):
\( 30 = 2(10 + z) \)

Step3: Solve for \( z \)

First, divide both sides by 2: \( \frac{30}{2}=10 + z \), so \( 15 = 10 + z \).
Then, subtract 10 from both sides: \( z = 15 - 10 = 5 \).

Answer:

5