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Question

Find the measure of each side of the triangle APQ if point B and point C are the mid points of the side AP and QA respectively.


Your Answer
A
AP = 6 cm
PQ = 8 cm
QA = 10 cm
Correct Answer
B
AP = 6 cm
PQ = 10 cm
QA = 8 cm
Your Answer
C
AP = 8 cm
PQ = 10 cm
QA = 6 cm
Your Answer
D
AP = 6 cm
PQ = 12 cm
QA = 8 cm

Solution

The correct option is B AP = 6 cm
PQ = 10 cm
QA = 8 cm
Given, 
AB = 3 cm, CA = 4cm and BC = 5 cm

Since, point B and point C are the mid points.
AB = BP = 3 cm
AP = AB + BP = 3 + 3 = 6 cm
also, QC = CA = 4 cm
QA = QC + CA = 4 + 4 = 8 cm

We know that the line segments joining the mid points of the two sides of a triangle is parallel to the third side and also half of it.
BC=PQ2
PQ=BC×2 = 5×2=10 cm

Therefore, measure of the sides are
AP = 6 cm
PQ = 10 cm
QA = 8 cm

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