Question

Refer to the diagram in which the medians of a triangle are shown.

Find the values of $x$and $y$ .

Short answer

$x=6,y=2.5$

Step-by-step solution

Step 1. Given information:

The given figure is:

Step 2. Concept used.

Centroid and median relation of a triangle.

Step 3. applying the concept.

As we know, the intersection of all the three medians of a triangle is called centroid of the triangle. Also, the centroid of a triangle divides the median in the ration 2 : 1.

From the given figure,

P is the centroid of the triangle since medians are given for the triangle.

Thus, from the centroid and median relation,

$\begin{array}{c}x:3=2:1\\ \frac{x}{3}=\frac{2}{1}\\ x=6\end{array}$

Similarly,

$\begin{array}{c}5:y=2:1\\ \frac{5}{y}=\frac{2}{1}\\ y=\frac{5}{2}\\ y=2.5\end{array}$

Therefore , the final answer is:

$x=6,\text{\hspace{0.17em}}y=2.5$