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Lines, Angles, and Triangles

SAT Math· difficulty 4/5

A right triangle has angles 30°30°, 60°60°, 90°90° and area 18sqrt318\\sqrt{3}. What is the length of the hypotenuse?

  • A

    12

    check_circle
  • B

    636\sqrt{3}

  • C

    838\sqrt{3}

  • D

    66

Explanation

Sides: a,asqrt3,2aa, a\\sqrt{3}, 2a. Area =frac12(a)(asqrt3)=fraca2sqrt32=18sqrt3= \\frac{1}{2}(a)(a\\sqrt{3}) = \\frac{a^2\\sqrt{3}}{2} = 18\\sqrt{3}, so a2=36a^2 = 36, a=6a = 6. Hypotenuse =12= 12.

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