Q. 74.7( 14 Votes )

The sides of a tr A. 16√5 cm

B. 10√5 cm

C. 24√5 cm

D. 28 cm

Answer :

a = 35, b = 54, c = 61

s = (a + b + c)/2


s = (35 + 54 + 61)/2 = 150/2 = 75.


Area(Δ) = √s(s-a)(s-b)(s-c)


Area(Δ) = √75(75-35)(75-54)(75-61)


Area(Δ) = √75×40×21×14


Area(Δ) = 420√5cm2


Area(Δ) = 1/2 × Base × Altitude


As the area of the triangle is fixed, for the longest altitude we need smallest base.


So, the length of base = 35cm


Area(Δ) = 1/2 × Base × Altitude


420√5 = 1/2 × 35 × Altitude


24√5 = Altitude.


Hence, the correct option is (C).

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