Help with Similarity Triangles Geometry. I dont understand how to solve for x on this one.

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asked Dec 26, 2023 32.9k views

24 votes

Help with Similarity Triangles Geometry. I dont understand how to solve for x on this-example-1

Mathematics
college

Davidsleeps asked

by Davidsleeps

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1 Answer

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since we know those two triangles are similar then we can use proportions.

$\cfrac{AE}{AB}=\cfrac{AD}{AC}\implies \cfrac{14-8}{2x}=\cfrac{14}{2x+4}\implies \cfrac{6}{2x}=\cfrac{14}{2x+4}\implies \cfrac{3}{x}=\cfrac{14}{2x+4} \\\\\\ 6x+12=14x\implies 12=8x\implies \cfrac{12}{8}=x\implies \cfrac{3}{2}=x \\\\[-0.35em] ~\dotfill\\\\ AB=2x+4\implies AB=2\left( (3)/(2) \right)+4\implies AB=3+4\implies AB=7$