27 The sides of a triangle are 10 cm, 24 cm and 26 cm Find its area and - Maths - Heron\s Formula

Question

27 The sides of a triangle are 10 cm, 24 cm and 26 cm Find its area
and the longest altitude

Varun.Rawat · Accepted Answer

Let a = 10 cm; b = 24 cm; c = 26 cm be the sides of the ∆
Semi-perimeter = a+b+c2 = 10+24+262 = 602 = 30 cmNow, area = ss-as-bs-c=3030-1030-2430-26=30×20×6×4=14400=120 cm2Now, longest altitude is made on shortest side
Now, area of ∆ = 12×base×altitude⇒120 = 12×10×altitude⇒5 altitude = 120⇒altitude = 1205 = 24 cmSo, longest altitude = 24 cm

27. The sides of a triangle are 10 cm, 24 cm and 26 cm. Find its area and the longest altitude.