Question

if dh = 4x - 10 and hf = x + 8, find the value of x for which defg must be a parallelogram.

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, if \(DEFG\) is a parallelogram, then \(DH = HF\). Given \(DH=4x - 10\) and \(HF=x + 8\), we set up the equation \(4x-10=x + 8\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(4x-x-10=x - x+ 8\), which simplifies to \(3x-10 = 8\). Then add 10 to both sides: \(3x-10 + 10=8 + 10\), giving \(3x=18\). Divide both sides by 3: \(\frac{3x}{3}=\frac{18}{3}\), so \(x = 6\).

Answer:

6