Gavin is in his office, deciding where to go to lunch. The distance from the deli to the coffee shop is 18 miles. The distance from Gavin’s office to the coffee shop is 24 miles. How many miles apart are the coffee shop and the pizza place?

30

Step-by-step explanation:

1.   24²+18²=900

2.  √900=30

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