Chapter 10.3, Problem 12WE

To determine

To calculate: value of $x$

Answer to Problem 12WE

  $x=4$ .

Explanation of Solution

Given information: $\overline{AU},\overline{BV}$ and $\overline{CW}$ are the medians of $\Delta ABC$ ; $AP=x^2$ and $PU=2x$ .

  

Calculation:

Medians divide the midpoint in the ratio $2:1$ from the vertex to the side.

From this,

Here, $\frac{AP}{PU}=\frac{2}{1}$ ,

  $\Rightarrow AP=2PU$ ,

  $\Rightarrow x^2=4x$ ,

  $\Rightarrow x=0$ or $x=4$ .

Since, $x=0$ is not possible (length can’t be zero), $x=4$ is the desired value.