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 B10.25 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(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 =61.5cm2 ∴Area ofΔABC=12×BC×AD [∵areaoftriangle=12(base×height)] 61.5=12×12×AD⟹AD=10.25 cm