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Lines, Angles, and Triangles

SAT Math· difficulty 4/5

In a right triangle, one leg is 3 more than the other. The hypotenuse is 15. What are the lengths of the legs?

  • A

    5 and 8

  • B

    9 and 12

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  • C

    6 and 9

  • D

    8 and 11

Explanation

Let legs be xx and x+3x+3. Then x2+(x+3)2=225x^2 + (x+3)^2 = 225, so 2x2+6x−216=02x^2 + 6x - 216 = 0, x2+3x−108=0x^2 + 3x - 108 = 0, (x−9)(x+12)=0(x-9)(x+12) = 0, so x=9x = 9. Legs: 9 and 12.

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