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Lines, Angles, and Triangles

SAT Math· difficulty 5/5

In triangle ABC, AD is the altitude from A to BC. If AB = 15, AC = 20, and BC = 25, what is the length of AD?

  • A

    12

    check_circle
  • B

    16

  • C

    144\sqrt{144}

  • D

    9

Explanation

Note 15-20-25 is 3-4-5 scaled, so triangle ABC is right-angled at A. Area =frac12(15)(20)=150= \\frac{1}{2}(15)(20) = 150. Also area =frac12(BC)(AD)=frac12(25)(AD)= \\frac{1}{2}(BC)(AD) = \\frac{1}{2}(25)(AD). So AD=frac30025=12AD = \\frac{300}{25} = 12.

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