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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.

A
10 cm
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B
10.25 cm
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C
10.5 cm
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D
10.75 cm
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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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