Question

The line SR passes through the centroid of the given triangle and meets the triangle at S on one side and the vertex R on the other side. Given PS = $2x$ and SQ = $4x-3$. Find the value of $x.$

• A. $1$ unit
• B. $1.5$ unit
• C. $3$ unit
• D. Insufficient data.

Answer 1

The correct option is B $1.5$ unit

In the given triangle, SR passes though one of the vertex and through the centroid and meets at the opposite side of the triangle.

We know that the median is a line from a vertex of a triangle to the midpoint of its opposite side.

Also, the centroid of a triangle is the point where the three medians coincide.

Hence, SR must be a median of the triangle.
$\therefore$ S is the midpoint of the the side PQ.
$\Rightarrow$ PQ = SQ
$\Rightarrow 2x=4x-3$
$\Rightarrow 3=4x-2x$
$\Rightarrow 3=2x$
​​​​​​​$\Rightarrow x=1.5$