The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is (a) 20 cm (b) 30 cm (c) 40 cm (d) 50 cm
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Let
a = 50cm
b = 78cm
c = 112
S = a+b+c/2
S = 50+78+112/2
S = 240/2 = 120
Area = \sqrt{s(s-a)(s-b)(s-c)}
= \sqrt{120(120-50)(120-78)(120-112)}
= \sqrt{2822400}
= 1680 cm^{2}
Longest side = 120cm
corresponding to this side as the base the altitude will be smallest.
area =1/2 x base x altitude
=1680 = 1/2 x 112 x altitude
=altitude = 1680 x 2/112
= 30cm
HOPE IT HELPS YOU :-)
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