Question

find the area of triangle whose sides are 15cm ,12cm and 9cm​

Answer 1

Question

1. Find the area of a triangle whose sides are 9 cm, 12 cm and 15 cm. Also, find the length of altitude corresponding to the largest side of the triangle.

Solution

Let a = 9 cm, b= 12 cm and c = 15 cm

$\sf{s=\dfrac{a+b+c}{2}=\dfrac{9+12+15}{2} \: cm=\dfrac{36}{2} \: cm=18 \: cm}$

$\sf{=>Area \: of \: triangle= \sqrt{s(s-a)(s-b)(s-c)} } \\ \sf{= \sqrt{18(18-9)(18-12)(18-15)}} \\ \sf{= \sqrt{18×9×6×3} = \sqrt{2916} =54 \: cm²}$

$\sf{Also, \: area \: of \: traingle=\dfrac{1}{2} \: base×corresponding \: altitude} \\ \sf{=>54=\dfrac{1}2}×15×h \\ \sf{=>h=\dfrac{54×2}{15} \: cm=7.2 \: cm}$