Question

The sides of triangle ABC are: AB = 6 cm,BC = 12 cm, AC = 10cm. K, M and P arethe midpoints of the sides AB, BC and AC respectivelyare the midpoints of the sides and the midpoints of the sides. Calculate the perimeter of KMP.

Answer 1

Answer: By inspecting the triangle we can come up with the following relationships, using the proportionality:

`\begin{gathered} (12)/(10)=(6)/(x)\rightarrow(1) \\ (12)/(6)=(6)/(y)\rightarrow(2) \\ (6)/(12)=(3)/(z)\rightarrow(3) \end{gathered}`

Solving the three equations, (1) (2) and (3) gives the answer for x,y,z which are the three sides of the smaller triangle, the steps are as follows:

`\begin{gathered} x=KM=5 \\ y=MP=3 \\ z=KP=6 \end{gathered}`

Therefore the perimeter is as follows:

`\begin{gathered} P=x+y+x=5+3+6=14 \\ P_((KMP))=14 \end{gathered}`