Q12. - Geometry

Question

$\overline{AU,}\overline{BV}$ and $\overline{CW}$ are the medians of$\Delta ABC$

If ${\text{AP=x}}^{\text{2}}\text{ and PU}=\text{2x, then x=?}$

Step-by-Step Solution

Answer

The value of $x$ is $4$.

Step 1. Given information.

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

Step 2. Concept Used.

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

Step 3. Let’s calculate the area & height of the rectangle.

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

From this,

Here, 

$\begin{array}{l}\frac{AP}{PU}=\frac{2}{1}\\ AP=2PU\\ x^2=4x\\ x=0orx=4\end{array}$

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