Question

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

Answer 1

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 :-)