Question

Construct the centroid of ΔPQR whose sides are PQ = 8cm; QR = 6cm;
RP = 7cm.​

Answer 1

Given:

The sides of Δ$PQR$ are $PQ=8cm$,$QR=6cm$ and $RP=7cm$.

To find:

We have to find the centroid of the Δ$PQR$ by constructing it.

Solution:

Firstly, take the side $PQ$ to be the base. (You can take any side to be the base as per your wish.)

Now, from the point $Q$ draw an arc of length $6cm$.

Then draw an arc of length $7cm$ keeping the compass on point $P$.

The point where these two arcs meet is point $R$. Then, Join point $R$ with points $P$ and $Q$.

A triangle with vertices $P$, $Q$ and $R$ with sides $PQ=8cm$ , $QR=6cm$, and $RP=7cm$ will be constructed.

Now construct a perpendicular bisector for all the sides.

The point inside the triangle where all these bisectors meet each other is known as the centroid of the triangle. Label it as Centroid.