A homeowner wishes to put a fence around a space in her yard to create a dog pen. The space that she wants to fence in is shown below where each unit on the graph represents one foot,
6
How many feet of fencing will the homeowner need to build the dog pen?
38 + 4V2
54
52
38 + 1072

 the answer is C 52

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