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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.

The sides of triangle ABC are: AB = 6 cm,BC = 12 cm, AC = 10cm. K, M and P arethe-example-1
User Amish
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1 Answer

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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}

User Hayonj
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6.7k points
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