Question

In the figure, M, N and P are the mid points of AB, AC and BC respectively. If MN = 3 cm, NP = 3.5 cm and MP = 2.5 cm, calculate BC, AB and AC.

Answer 1

In $\Delta ABC$

M,N and P are the mid points of side, AB, AC and BC respectively.

MN = 3 cm, NP = 3.5 cm

MP = 2.5 cm

$\because$ M and N are the mid points of AB and AC

$\therefore$ MN || BC and $MN=\frac{1}{2}BC$

$\Rightarrow 3=\frac{1}{2}BC$

$\therefore BC=6cm$

Similarly, we can prove then

$NP=\frac{1}{2}AB$

$\Rightarrow AB=2\times NP=2\times 3.5=7cm$

and $MP=\frac{1}{2}AC$

$\Rightarrow AC=2\times MP=2\times 2.5=5cm$

Hence BC = 6cm , AB = 7cm and AC = 5cm