Question

if gh = gj = 17, hi = 5z, and ij = z + 16, what is the value of z?

Explanation:

Step1: Set up equation

Since $HI = IJ$ (properties of kite - like figure), we have $5z=z + 16$.

Step2: Solve for z

Subtract $z$ from both sides: $5z - z=z + 16 - z$, $4z = 16$. Then divide by 4: $z=\frac{16}{4}=4$.

Answer:

$z = 4$