Question

if the perimeter of the parallelogram is 100, find the lengths of the sides.
x 2x - 8 y
x + 4
w z
a. 22 and 28
b. 18 and 15
c. 14 and 12
d. 24 and 22

Explanation:

Step1: Recall parallelogram side - length property

In a parallelogram, opposite sides are equal. So the perimeter $P = 2(x + 4)+2(2x - 8)$.

Step2: Set up the perimeter equation

We know that $P = 100$. So, $2(x + 4)+2(2x - 8)=100$.
First, distribute the 2s: $2x+8 + 4x-16 = 100$.
Combine like - terms: $(2x + 4x)+(8 - 16)=100$, which simplifies to $6x-8 = 100$.

Step3: Solve for x

Add 8 to both sides of the equation: $6x-8 + 8=100 + 8$, giving $6x = 108$.
Divide both sides by 6: $x=\frac{108}{6}=18$.

Step4: Find the side lengths

One side length is $x + 4$. Substitute $x = 18$ into it, we get $18 + 4=22$.
The other side length is $2x - 8$. Substitute $x = 18$ into it, $2\times18-8=36 - 8 = 28$.

Answer:

A. 22 and 28