Main ASSE
The highway loop around a major city can be modeled by a circle with a circumference of 53 miles. The
distance across the city represents the diameter of the circle. Which distance is closest to the distance
across the city?
A. 106 miles
B. 53 miles
C. 27 miles
D. 17 miles

Step-by-step explanation:

Given

Required

Determine the diameter (D)

In terms of diameter, circumference is calculated as thus:

Take as 3.14 and substitute 53 for C

Make D the subject

--- Approximated

Hence,

Option D answers the question

uhhh idk u yolo?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4