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.10 cm10.25 cm10.5 cm10.75 cm

Solution

## The correct option is B 10.25 cmGiven, 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(s−a)(s−b)(s−c)    [by Heron’s formula] =√18(18−11)(18−12)(18−13) =√18×7×6×5 =√3×6×7×6×5 =6√3×7×5 =6√105=6×10.25 =61.5 cm2 ∴Area of ΔABC=12×BC×AD [∵ area of triangle=12(base×height)] 61.5=12×12×AD⟹AD=10.25 cm

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