Question

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

If $PB=1.9,$then $AB=?,AP=?$ .

Short answer

$AP=3.8,AB=5.7$

Step-by-step solution

Step 1. Given information:

Medians of the triangles are shown in the given figure:

$PB=1.9$

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

Here,

role="math" localid="1649119919240" $\frac{AP}{PB}=\frac{2}{1}$

$\begin{array}{c}\therefore AP=\frac{2}{1}\times 1.9\\ =3.8\\ AB=AP+PB\\ =3.8+1.9\\ =5.7\end{array}$

Therefore the final answer is $5.7$