Question

find the area of triangle whose sides are 42cm,34cm and 20cm in length. hence ,find the height corresponding to the longest side.

Answer 1

Take a=11 cm, b=8 cm, c=13 cmThe semi perimeter is given by, s=a+b+c2 =11 cm+8 cm+13 cm2 =322cm =16 cmThe area of the traingle is given by Heron's formula, Area△=s s-a s-b s-c =16 16-11 16-8 16-13 =16 5 8 3 =2×2×2×2 5 2×2×2 3 =2×2×22×3×5 =830 cm2Note that the area of △ABC is also given by the formula, area △=12×base×altitude area △=12×c×altitude Substitute the values to get, 830 =12×13×altitude altitude= 2× 83013 = 163013 =6.74cm approx