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Lines, Angles, and Triangles

SAT Math· difficulty 4/5

A right triangle has legs in the ratio 5:125:12. If the hypotenuse is 26, what is the length of the longer leg?

  • A

    169\sqrt{169}

  • B

    13

  • C

    24

    check_circle
  • D

    10

Explanation

Legs are 5k5k and 12k12k. Then (5k)2+(12k)2=262(5k)^2 + (12k)^2 = 26^2, so 169k2=676169k^2 = 676, k2=4k^2 = 4, k=2k = 2. Longer leg =12(2)=24= 12(2) = 24.

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