HardMath· Geometry and Trigonometry· Lines, angles, and triangles· SPR
The area of triangle ABC above is at least 48 but no more than 60. If y is an integer, what is one possible value of x ?
Correct answer: 10/3 or 15/4 or 25/6
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Explanation
The correct answer is either , , or . The area of triangle ABC can be expressed as or . It’s given that the area of triangle ABC is at least 48 but no more than 60. It follows that . Dividing by 6 to isolate y in this compound inequality yields . Since y is an integer, . In the given figure, the two right triangles shown are similar because they have two pairs of congruent angles: their respective right angles and angle A. Therefore, the following proportion is true: . Substituting 8 for y in the proportion results in . Cross multiplying and solving for x yields . Substituting 9 for y in the proportion results in . Cross multiplying and solving for x yields . Substituting 10 for y in the proportion results in . Cross multiplying and solving for x yields . Note that 10/3, 15/4, 25/6, 3.333, 3.75, 4.166, and 4.167 are examples of ways to enter a correct answer.
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id cb_question_bank:84122363-e5b6-464c-a789-05363f3f1e60 · question eeb4143c · IBN 070631-DC
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