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.
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=30 cm2 ......(i)
Let p be the length of the perpendicular from vertex A on the side BC. Then,
A=12×(13)×p .........(ii)
From (i) and (ii) we get
12×(13)×p=30⇒p=6013 cm
∴,m=60
Hence, m÷10=60÷10=6.