In a ÔÅÑabc , ab = 10 cm, bc = 12 cm and ac = 18 cm. find the length of smallest altitude
Answers
Given : Δabc ab = 10 cm, bc = 12 cm and ac = 18 cm.
To find : the length of smallest altitude
Solution:
using heron formula for area of triangle
a = 12 cm , c = 10 cm b = 18 cm
s = ( a + b + c)/2 = ( 12 + 10 + 18) /2 = 20 cm
Area of triangle = √s(s - a)(s-b)(s-c)
= √20(20 - 12)(20-10)(20 - 18)
= √20 * 8 * 10 * 2
= √20 * 2 *2 * 2 * 20
= 40 √2 cm²
smallest altitude will be on longest side
Area of triangle = (1/2) * base * altitude
= (1/2) * 18 * altitude = 40 √2
=> altitude = 40 √2/9
=> altitude = 6.28 cm
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