Question

the side of a triangle are 35cm ,54cm,61cm,respectively. find the length of longest altitude.
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Answer 1

a = 35, b = 54, c = 61 s = (a + b + c)/2 ⇒ s = (35 + 54 + 61)/2 = 150/2 = 75. Area(Δ) = √s(s-a)(s-b)(s-c) ⇒ Area(Δ) = √75(75-35)(75-54)(75-61) ⇒ Area(Δ) = √75×40×21×14 ⇒ Area(Δ) = 420√5 cm2 Area(Δ) = 1/2 × Base × Altitude As the area of the triangle is fixed, for the longest altitude we need smallest base. So, the length of base = 35cm Area(Δ) = 1/2 × Base × Altitude ⇒ 420√5 = 1/2 × 35 × Altitude ⇒ 24√5 = Altitude.Read more on Sarthaks.com - https://www.sarthaks.com/874705/the-sides-triangle-are-35-cm-54-cm-and-61-cm-respectively-the-length-of-its-longest-altitude