Answer:
D. 256 feet
Step-by-step explanation:
We are solving for the diameter, but first let's get the radius, which is either AC or AD.
Let's think about this in terms of the triangles: what do we know? Both triangles are right triangles, which means we can apply the Pythagorean Theorem:
[tex]a^{2} + b^{2} = c^{2}[/tex] , where a and b are legs and c is the hypotenuse.
Let's focus on the left triangle, ACE.
- We can figure out that CE = 100 ft because CD = 200, and CE is half of CD.
- We were given that AE = 80 ft.
- Now all that's left is AC, which we can solve for.
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]100^{2} + 80^{2} = c^{2}[/tex]
16400 = [tex]c^{2}[/tex]
[tex]\sqrt{16400} = \sqrt{c^{2} }[/tex]
c = 128.06 = AC
AC is the radius, which is half the diameter, so the diameter is 128.06*2 = 256.12 = about 256 feet.
