ShmoopTube

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Here’s your shmoop du jour, brought to you by triangles of all shapes and sizes.

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Triangle ABC is similar to triangle EDC, which is also similar to triangle EFG.

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Find the perimeter of triangle EFG.

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Here are the potential answers...

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They’ve gotten us off to a slow start… all we know is that side FG is “1.”

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Now how do we find FE and EG?

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What do we know about similar triangles?

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All corresponding angles are equal from one to the next…okay, good to know…

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…and the other thing is that all corresponding sides have a relative length.

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In other words, if the length of one side is doubled, then the lengths of all sides are doubled.

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Triangle ABC isn’t going to help us much at the moment…

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…because although two of its sides are labeled, it’s missing the one that we do have for triangle EFG.

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Whereas, with triangle EDC, the side that is labeled as “3” directly corresponds to side FG.

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So now we know that everything in triangle EDC is triple that of triangle EFG.

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We also know that line CE is 2.25…so if the corresponding side in triangle EFG, side

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EG, is one-third of that length… it must be 0.75 units in length.

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All right…now we can see the relationship between triangles EFG and ABC.

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Looks like ABC is twice as large as its counterpart to the right.

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In that case, since line AB is “2,” line EF must be “1.”

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And now it’s just a case of adding ‘em up… 1 plus 1 plus 0.75 = 2.75…

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…answer A.

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