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 property

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

Step2: Set up the perimeter equation

We know that \(P = 100\), so \(2(2x - 8)+2(x + 4)=100\). First, distribute the 2s: \(4x-16 + 2x+8 = 100\).

Step3: Combine like - terms

Combine the \(x\) terms and the constant terms: \((4x + 2x)+(-16 + 8)=100\), which simplifies to \(6x-8 = 100\).

Step4: Solve for \(x\)

Add 8 to both sides of the equation: \(6x-8 + 8=100 + 8\), getting \(6x=108\). Then divide both sides by 6: \(x=\frac{108}{6}=18\).

Step5: Find the side lengths

One side length is \(x + 4\), substituting \(x = 18\), we get \(18 + 4=22\). The other side length is \(2x-8\), substituting \(x = 18\), we have \(2\times18-8=36 - 8 = 28\).

Answer:

A. 22 and 28