Answer:
- [tex]s=\frac{P}{3}[/tex]
- Dimensions of the flag:
[tex]lenght=6.65\ ft\\\\width=3.5\ ft[/tex]
- Area of the flag: [tex]23.275\ ft^2[/tex]
Step-by-step explanation:
The missing figure of the exercise is attached.
We know that the perimeter of the triangle is given by:
[tex]P= 3s[/tex]
Where "s" is the side lenght of the triangle.
Solving for "s", we get:
[tex]s=\frac{P}{3}[/tex]
Therefore, if the perimeter of the triangle is 126 inches, its side length is:
[tex]s=\frac{126\ in}{3}\\\\s=42\ in[/tex]
Since [tex]1\ ft=12\ in[/tex], we know that "s" in feet is:
[tex]s=(42\ in)(\frac{1\ ft}{12\ in})=3.5\ ft[/tex]
The area of a rectangle can be calculated with this formula:
[tex]A=lw[/tex]
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:
[tex]l=1.9s\\w=s[/tex]
Then, the dimensions of the flag are:
[tex]l=1.9(3.5\ ft)=6.65\ ft\\w=3.5\ ft[/tex]
And the area is:
[tex]A=(6.65\ ft)(3.5\ ft)=23.275\ ft^2[/tex]
