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Question

In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. Find the length of the altitude corresponding to the side having 12 cm.
  1. 10 cm
  2. 10.25 cm
  3. 10.5 cm
  4. 10.75 cm


Solution

The correct option is B 10.25 cm
Given, the sides of a triangle are:
a = 11 cm, b = 12 cm  and c = 13 cm.
Now, semi-perimeter,
s=a+b+c2
=11+12+132=362=18 cm
Area of triangle =s(sa)(sb)(sc)    [by Heron’s formula]
=18(1811)(1812)(1813)
=18×7×6×5
=3×6×7×6×5
=63×7×5
=6105=6×10.25
=61.5 cm2
Area of ΔABC=12×BC×AD
[ area of triangle=12(base×height)]
61.5=12×12×ADAD=10.25 cm


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