The scale on a map reads ½ inch = 30 miles. If two cities on the
map are 5 ¾ inches apart, find
the actual distance between the
cities.

Answer

172.5mi

Step-by-step explanation:

5 inches (30) = 150,  = 1/2 inch=30, half of the half = 30

5x30+30+15

80 the answer is 80

step-by-step explanation:

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