Note: I had to write FA in that order, and not the other way around, due to the filter.
Part 1
There are 2 answers and they are
- Choice 2) FA/AB = FG/BC
- Choice 3) AB/FA= BC/FG
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Explanation:
For any of the answer choices we are involving the following segments
So we're only involving four segments. They are paired up to form fractions which are then set equal to one another. Notice how segment FA is smaller than AB, and how they correspond together. Going from FA to AB means go from small to big. If we write the ratio FA/AB, then can think of it as small/big.
Also note that FG is smaller than BC, and both segments also correspond as they are both going downhill from left to right. So we can write FG/BC to set equal to the first fraction we set up.
Overall, the proportion FA/AB = FG/BC is one valid answer.
The other valid answer is AB/FA= BC/FG. This equation is formed by applying the reciprocal to both sides of the first equation mentioned.
We can rule out choice 1 because FA/AB is small/big, but BC/FG is big/small. The two don't match up. Choice 4 is ruled out because AB does not correspond to FG.
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Part 2
<h3>Answer: 27</h3>
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Explanation:
Through similar ideas mentioned in part 1, we can form this proportion
FA/AB = AG/AC
we have the format small/big = small/big
We are given these values either in word form or through the diagram
- FA= 15
- AB = FA+FB = 15+30 = 45
- AC = 81
Plug in those given values and isolate AG
FA/AB = AG/AC
15/45 = AG/81
15*81 = 45*AG .... cross multiply
1215 = 45AG
45AG = 1215
AG = 1215/45 .... divide both sides by 45
AG = 27
Segment AG is 27 inches long.
