Question

if (vy = xy = 24), (vw = 4p), and (wx = p + 27), what is (vw?
vw=)

Explanation:

Step1: Apply perpendicular - bisector theorem

Since $WY$ is perpendicular to $VX$ and $VY = XY$, by the perpendicular - bisector theorem, $VW=WX$.

Step2: Set up the equation

Set $4p=p + 27$.

Step3: Solve for $p$

Subtract $p$ from both sides: $4p−p=p + 27−p$, which gives $3p=27$. Then divide both sides by 3: $p=\frac{27}{3}=9$.

Step4: Find $VW$

Since $VW = 4p$ and $p = 9$, then $VW=4\times9 = 36$.

Answer:

36