2009 AMC 10A Problem 12 — Solution | LIVE by Po-Shen Loh

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2009 AMC 10A Problem 12

Attempt Problem 12 of the 2009 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 10A solutions, or check the answer key.

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12.

In quadrilateral $ABCD,$ $AB = 5,$ $BC = 17,$ $CD = 5,$ $DA = 9,$ and $BD$ is an integer. What is $BD?$

$11$

$12$

$13$

$14$

$15$

Answer: C

Concepts:triangle inequality bounding to limit cases

Difficulty rating: 1220

Solution:

In $\triangle BCD,$ the triangle inequality gives $5 + BD \gt 17,$ so $BD \gt 12.$

In $\triangle ABD,$ it gives $5 + 9 \gt BD,$ so $BD \lt 14.$

The only integer with $12 \lt BD \lt 14$ is $BD = 13.$

Thus, the correct answer is C.

← Problem 11#11

Problem 13#13 →

Problem 12 in Other Years

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