ShmoopTube

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Here's your shmoop du jour: What is the perimeter of triangle GHF?

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And here are the potential answers...

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First let's be clear that it's THIS triangle we're talking about -- so....why would

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the question SHOW us all this other stuff?

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Hm...

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Yeah. Well -- FGH and FDE are SIMILAR triangles -- that is, all their angles are equal, and

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GH is parallel to DE.

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How do we know? Well, since the two triangles are SIMILAR, it means that the perimeter edges

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must parallel.

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Start by finding the perimeter of triangle FDE...

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We get 8 plus 2 plus 6 plus 2 plus 8... which is 26.

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We want to find GH and we know that GH is proportional to DE.

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So we can write FG is to FD, or 8 is to 10, as GH is to DE -- and DE is 6... so we get

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the ratio 8 is to 10 as GH is to 6.

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Cross-multiply and we get 48 equals 10 times GH... so the distance GH is 48 over 10...

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or 4.8.

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Now we have to just add the perimeter sides of 8 and 8 which is 16; add to 4.8 and we

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get 20.8 as the perimeter for triangle GHF.

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Answer D.

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