AMC 10 Step by Step
Log inSign up
Printable

2017 AMC 10A Problem 21

Include the solutionBack to the problem
2017 AMC 10A Problem 21AMC 10 Step by Step
Name:                             Date: September 13, 2026
Similar & Congruent Triangles · difficulty 4 of 5 · about 7 min · position P21-25

A square with side length xx is inscribed in a right triangle with sides of length 33 , 44 , and 55 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length yy is inscribed in another right triangle with sides of length 33 , 44 , and 55 so that one side of the square lies on the hypotenuse of the triangle. What is xy\tfrac{x}{y} ?

  1. A)

    1213\dfrac{12}{13}

  2. B)

    3537\dfrac{35}{37}

  3. C)

    11

  4. D)

    3735\dfrac{37}{35}

  5. E)

    1312\dfrac{13}{12}

Working