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Lines, angles, and triangles SAT question
Math · Geometry and Trigonometry · Hard · Answer it here, explanation included.
In the figure above,
and
. What is the length of
?
Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.
ExplanationShow
The correct answer is 4.5. According to the properties of right triangles, BD divides triangle ABC into two similar triangles, ABD and BCD. The corresponding sides of ABD and BCD are proportional, so the ratio of BD to AD is the same as the ratio of DC to BD. Expressing this information as a proportion gives 
. Solving the proportion for DC results in
. Note that 4.5 and 9/2 are examples of ways to enter a correct answer.
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