Question

In the given 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, find the sum of the lengths of $BC+AB+AC.$

• A. 18

Answer 1

The correct option is A 18
Here, MN is a line which joins the mid-point M of AB and N of AC.

Then, by mid-point theorem, $MN\parallel BC\text{and}MN=\frac{1}{2}BC$
$\Rightarrow BC=2MN=6cm$

$\text{Similarly,}AC\parallel MP\text{and}MP=\frac{1}{2}AC$
$\Rightarrow AC=2MP=5cm$

$\text{And,}AB\parallel NP\text{and}NP=\frac{1}{2}AB$
$\Rightarrow AB=2NP=7cm$

So, the length of the sides BC, AB and AC are 6 cm, 7 cm and 5 cm respectively.

$\Rightarrow BC+AB+AC=6cm+7cm+5cm=18cm$