Given:
a triangle is given as below
Find:
we have to find the length of the vertical support.
Explanation:
Firstly we will find the area of triangle using Heron's formula as below
[tex]Area=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
where 's' is semi-perimeter of the triangle.
[tex]s=\frac{13.6+4.4+14.3}{2}=16.15\text{ }ft[/tex]
Therefore, area of the given triangle is
[tex]\begin{gathered} Area=\sqrt{16.15(16.15-13.6)(16.15-4.4)(16.15-14.3)} \\ Area=\sqrt{16.5\times2.55\times11.75\times1.85} \\ Area=\sqrt{914.6053125} \\ Area=30.24\text{ }ft^2(approximately) \end{gathered}[/tex]
Let 'x' be the length of the vertical support (which is height of the triangle)
Now, area of a triangle is equal to (1/2)*base*height.
[tex]\begin{gathered} 30.24=\frac{1}{2}\times14.3\times x \\ x=\frac{30.24\times2}{14.3} \\ x=4.2\text{ }ft(approximately) \end{gathered}[/tex]
Therefore, The approximate length of the support is about 4.2 ft.
So, C is the correct option.
