Question

The length of the sides of a triangle are 8cm, 12cm , 16cm. Find the height of the corresponding to the longest side

Answer 1

s=a+b+c/2
18+12+16/2=36/2=18
area=1/2×b×h
18=1/2×8
h=18×2/8
=3

Answer 2

Answer:

The height is 5.81 cm

Step-by-step explanation:

Given the length of the sides of a triangle are 8 cm, 12 cm , 16 cm.

we have to find the height of the corresponding to the longest side.

$s=\frac{a+b+c}{2}=\frac{8+12+16}{2}=\frac{36}{2}=18 cm$

By Heron's formula

$Area=\sqrt{s(s-a)(s-b)(s-c)}$

$\frac{1}{2}\times base\times height=\sqrt{18(18-8)(18-12)(18-16)}$

$\frac{1}{2}\times BC\times AD=\sqrt{18\times 10\times 6\times 2}$

$\frac{1}{2}\times 16\times h=12\sqrt{15}$

$h=\frac{12\sqrt{15}}{8}=\frac{3\sqrt{15}}{2}=5.81 cm$

Hence, the height is 5.81 cm