Question

Which is greater the premiere or the flag circumference of the cannons mouth ( flag 10, 8 in ( cannon 9in

Answer 1

the flag is right angle triangle,

it base = 8 in

hypotenuse = 10 in

we know the Pythagoras theorem,

$\text{base}^2+\text{perpendicular}^2=\text{hypotenuse}^2$$\begin{gathered} 8^2+\text{perpendicular}^2=10^2 \\ \text{perpendicular}^2=100-64 \\ \text{perpendicular}^2=36 \end{gathered}$

take root both side,

$\begin{gathered} \text{perpendicular}^{}=\sqrt{36} \\ \\ \text{perpendicular}=6 \end{gathered}$

so the perimeter of the flag is, = sum of all sides

6 + 8 + 10 = 24 inches,

For the Canon mouth,

it has the shape of circle,

so, radius is r = 9 in

the circumference is,

$=2\times\pi\times r$$\begin{gathered} =2\times\frac{22}{7}\times9 \\ =56.57 \end{gathered}$

so the circumference of the canon's mouth is 56.57 inches,

thus, canon's mouth circumference is greater than the perimeter of the flag