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2005 AMC 10A Problem 19

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2005 AMC 10A Problem 19AMC 10 Step by Step
Name:                             Date: September 13, 2026
Triangles: Area & Pythagorean · difficulty 3 of 5 · about 5 min · position P16-20

Three one-inch squares are placed with their bases on a line. The center square is lifted out and rotated 45∘45^{\circ} , as shown. Then it is centered and lowered into its original location until it touches both of the adjoining squares. How many inches is the point BB from the line on which the bases of the original squares were placed?

figure

  1. A)

    11

  2. B)

    2\sqrt{2}

  3. C)

    32\frac{3}{2}

  4. D)

    2+12\sqrt{2}+\frac{1}{2}

  5. E)

    22

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