if the sides of a triangle is 20 units, 21 units snd 29 units. then sum kf the altitudes of triangle is
Answers
Given : sides of a triangle is 20 units, 21 units and 29 units
To Find : sum of the altitudes of triangle
Solution:
Sides of triangle are
20 , 21 & 29 units
s = (20 + 21 + 29)/2 = 35
Area of Triangle = √(35(35 - 20)(35-21)(35 - 29))
= √35(15)(14)(6)
= √(5*7((5*3)(7*2)(2*3)
= 2 * 3 * 5 * 7
= 210 sq units
Area of triangle = (1/2) (20) * Altitude 1 = 210 => Altitude 1 = 21
(1/2) (21) * Altitude 2 = 210 => Altitude 2 = 20
(1/2) (29) * Altitude 3 = 210 => Altitude 3 = 420/29 = 14.48 cm
sum of the altitudes of triangle = 21 + 20 + 14.48 = 55.48 cm
or 1609/29 cm
55.48 cm is the sum of the altitudes of triangle
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