Find the area of ΔABC in which AB = 36 cm, BC = 48 cm and AC = 60 cm. Also, find the length of the shortest altitude.
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If a,b,c are the sides of a triangle and s is the semi perimeter, then area is-
A = √s (s-a) (s-a) (s-c)
A = 36, B = 60, C = 48
s (semi-perimeter) = 1/2 (36+60+48) = 72
A = √s (s-a) (s-b) (s-c) = √ 72 × (72-36) × (72-60) × (72-48)
A = √ 72 × 36 × 12 × 24 = 864 cm^2
Finding the length of shortest altitude
A = 1/2 × Base × Height
864 = 1/2 × 48 × H
864 = 24 × H
864/24 = H
36 = H
A = √s (s-a) (s-a) (s-c)
A = 36, B = 60, C = 48
s (semi-perimeter) = 1/2 (36+60+48) = 72
A = √s (s-a) (s-b) (s-c) = √ 72 × (72-36) × (72-60) × (72-48)
A = √ 72 × 36 × 12 × 24 = 864 cm^2
Finding the length of shortest altitude
A = 1/2 × Base × Height
864 = 1/2 × 48 × H
864 = 24 × H
864/24 = H
36 = H
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