Question

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

If $AB=6,$then $BP=?,AP=?$ .

Short answer

$BP=2,AP=4$

Step-by-step solution

Step 1. Given information:

Medians of the triangles are shown in the given figure:

Step 2. Concept used.

Centroid and median relation of a triangle.

Step 3. applying the concept.

Medians divide the midpoint in the ratio $2:1$

Here,$\frac{AP}{BP}=\frac{2}{1}$

Thus,$AP=2BP$.

Also,

$\begin{array}{c}AB=AP+BP\\ =3BP\\ BP=\frac{AB}{3}\\ =2\end{array}$

Hence,$AP=2BP=4$