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(s−a)(s−b)(s−c) =√15(15−5)(15−12)(15−13) ⇒A=√15×10×3×2=30cm2
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=30⇒p=6013cm
Hence m÷10=60÷10=6.