Question 9
Write True or False and justify your answer:
In a triangle, the sides are given as 11cm, 12cm and 13cm. the length of the altitude is 10.25 cm corresponding to the side having 12 cm.
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Solution
True Since the sides of a triangle are a = 11cm, b = 12cm and c = 13cm. Now, semi-perimeter, s=a+b+c2 =11+12+132=362=18m 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 ∴AreaofΔABC=12×BC×AD [∵areaoftriangle=12(base×height)] =12×12×10.25=6×10.25=61.5cm2