Question

10. Make Sense and Persevere The flag of the

Bahamas includes an equilateral triangle. The
perimeter of the triangle is P= 3s, where s is
the side length. Solve for s. Use your formula to
find the dimensions of the flag in feet and the
area in square feet when the perimeter of the
triangle is 126 inches.

Answer 1

• 
  `s=(P)/(3)`
• Dimensions of the flag:

`lenght=6.65\ ft\\\\width=3.5\ ft`

• Area of the flag:
  `23.275\ ft^2`

Explanation:

The missing figure of the exercise is attached.

We know that the perimeter of the triangle is given by:

`P= 3s`

Where "s" is the side lenght of the triangle.

Solving for "s", we get:

`s=(P)/(3)`

Therefore, if the perimeter of the triangle is 126 inches, its side length is:

`s=(126\ in)/(3)\\\\s=42\ in`

Since
`1\ ft=12\ in`, we know that "s" in feet is:

`s=(42\ in)((1\ ft)/(12\ in))=3.5\ ft`

The area of a rectangle can be calculated with this formula:

`A=lw`

Where "l" is the lenght and "w" is the width

We can observe in the figure that the lenght and the width of the flag are:

`l=1.9s\\w=s`

Then, the dimensions of the flag are:

`l=1.9(3.5\ ft)=6.65\ ft\\w=3.5\ ft`

And the area is:

`A=(6.65\ ft)(3.5\ ft)=23.275\ ft^2`