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Lines, Angles, and Triangles

SAT Math· difficulty 3/5

An isosceles right triangle has hypotenuse 1010. What is its area?

  • A

    502\frac{50}{\sqrt{2}}

  • B

    50

  • C

    25225\sqrt{2}

  • D

    25

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Explanation

Each leg =frac10sqrt2=5sqrt2= \\frac{10}{\\sqrt{2}} = 5\\sqrt{2}. Area =frac12(5sqrt2)(5sqrt2)=frac12(50)=25= \\frac{1}{2}(5\\sqrt{2})(5\\sqrt{2}) = \\frac{1}{2}(50) = 25.

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