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Question

The lengths of the sides of a triangle are 5 cm, 12 cm and 13 cm. The length of the perpendicular from the opposite vertex to the side whose length is 13 cm is m13. Find the value of m÷10.

A
6
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B
60
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C
5
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D
13
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Solution

The correct option is A 6
Here, a = 5, b = 12 and c = 13.
s=12(a+b+c)=12(5+12+13)=15.
Let A be the area of the given triangle.
Then,
A=s(sa)(sb)(sc)
=15(155)(1512)(1513)
A=15×10×3×2=30 cm2

Let p be the length of the perpendicular from vertex A to the side BC. Then,
A=12×(13)×p
From (i) and (ii) we get
12×(13)×p=30p=6013 cm
Hence m÷10=60÷10=6.

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