Respuesta :
The company decides to make just three sizes of tents: the Mini, the Twin, and the Family-Size.
The shape of these tents is an equilateral triangle.
Part 1:
For the Twin, each edge of the triangle will be 8 ft.
The height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Where a is the length of the edge of the triangle.
Since we are given that a = 8 ft
[tex]\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=8\cdot\frac{\sqrt[]{3}}{2} \\ h=4\sqrt[]{3} \\ h=6.9\: ft \end{gathered}[/tex]Therefore, the height of the Twin tent at the center is 6.9 ft
Part 2:
The Mini tent will have edges 5 ft long.
The height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Where a is the length of the edge of the triangle.
Since we are given that a = 5 ft
[tex]\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=5\cdot\frac{\sqrt[]{3}}{2} \\ h=4.3\: ft \end{gathered}[/tex]Therefore, the height of the Mini tent at the center is 4.3 ft
Part 3:
The Family-Size tent will have a height of 10 ft at the center.
Recall that the height of the tent is given by
[tex]h=a\cdot\frac{\sqrt[]{3}}{2}[/tex]Re-writing the formula for edge (a)
[tex]a=h\cdot\frac{2}{\sqrt[]{3}}[/tex]Since we are given that h = 10 ft
[tex]\begin{gathered} a=h\cdot\frac{2}{\sqrt[]{3}} \\ a=10\cdot\frac{2}{\sqrt[]{3}} \\ a=\frac{20}{\sqrt[]{3}} \\ a=11.6\: ft \end{gathered}[/tex]Therefore, the length of edges of the Family-Size tent is 11.6 ft
