Chapter 10.3, Problem 2WE

To determine

To find: the values of x and y from the given figure .

Answer to Problem 2WE

  $x=6,\text{}y=2.5$

Explanation of Solution

Given:

The given figure is:

  

Concept used:

Centroid and median relation of a triangle.

Calculation:

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 values of x and y are 6 and 2.5 respectively.

Conclusion:

  $x=6,\text{}y=2.5$