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Lines, angles, and triangles SAT question

Math · Geometry and Trigonometry · Medium · Answer it here, explanation included.

The figure presents quadrilateral A, C D F, where side A, F and side C D are horizontal, and side C D lies above side A, F. Side C D is longer than side A, F. Point B lies on left side A, C, and point E lies on right side D F. Line segment B E, which is horizontal, divides quadrilateral A, C D F into two quadrilaterals, A, B E F and B C D E.

In the figure above, $side A, F$ , $line segment B E$ , and $side C D$ are parallel. Points B and E lie on $side A, C$ and $side F D$ , respectively. If $the length of line segment A, B equals 9, the length of line segment B C equals 18 point 5$ , and $the length of line segment F E equals 8 point 5$ , what is the length of $line segment E D$ , to the nearest tenth?

ExplanationShow

Choice B is correct. Since $line segment A F$ , $line segment B E$ , and $line segment C D$ are parallel, quadrilaterals $A F E B$ and $B E D C$ are similar. Let x represent the length of $line segment E D$ . With similar figures, the ratios of the lengths of corresponding sides are equal. It follows that $9 over 18 point 5, equals 8 point 5 over x$ . Multiplying both sides of this equation by 18.5 and by x yields $9 x equals, 18 point 5, times 8 point 5$ , or $9 x equals 157 point 2 5$ . Dividing both sides of this equation by 9 yields $x equals 17 point 4 7$ , which to the nearest tenth is 17.5.

Choices A, C, and D are incorrect and may result from errors made when setting up the proportion.

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Lines, angles, and triangles SAT question

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