Question

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

4. If $AB=7,$then $BP=?,AP=?$ .

Short answer

$BP=2.33,AP=4.67$

Step-by-step solution

Step 1. Given information:

Medians of the triangles are shown in the given figure:

$AB=7$

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, role="math" localid="1649119456316" $\frac{AP}{BP}=\frac{2}{1}$

$AP=2BP.$

Also,

$\begin{array}{c}AB=AP+BP\\ =3BP\\ BP=\frac{AB}{3}\\ =2.33\\ AP=2BP\\ =4.67\end{array}$