Question

Tents-R-Us makes and sells tents. Tents-R-Us' motto is“Keep It Simple.” The company decides to makes justthree sizes of tents: the Mini, the Twin, and theFamily-Size. All the tents they make have equilateraltriangular ends as shown at right.1. For the Twin, each edge of the triangle will be 8 ft. Find the heightof the tent at the center, correct to the nearest inch. One way to findthis height is to make an accurate scale drawing and measure.

Answer 1

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

`h=a\cdot\frac{\sqrt[]{3}}{2}`

Where a is the length of the edge of the triangle.

Since we are given that a = 8 ft

`\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}`

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

`h=a\cdot\frac{\sqrt[]{3}}{2}`

Where a is the length of the edge of the triangle.

Since we are given that a = 5 ft

`\begin{gathered} h=a\cdot\frac{\sqrt[]{3}}{2} \\ h=5\cdot\frac{\sqrt[]{3}}{2} \\ h=4.3\: ft \end{gathered}`

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

`h=a\cdot\frac{\sqrt[]{3}}{2}`

Re-writing the formula for edge (a)

`a=h\cdot\frac{2}{\sqrt[]{3}}`

Since we are given that h = 10 ft

`\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}`

Therefore, the length of edges of the Family-Size tent is 11.6 ft