Here is a map of the Missouri Botanical Garden. Clare walked all the way around the garden. The map shows a scale measure that represents 0, 300, and 600 feet.
What is the actual distance around the garden? Show your reasoning.
It took Clare 30 minutes to walk around the garden at a constant speed. At what speed was she walking? Show your reasoning.

angle addition postulate

2x=56

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