2022 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 2 Easy

In rhombus ABCD, point P lies on segment \overline{AD} such that BP\bot AD, AP=3 and PD=2. What is the area of ABCD? (Note: The figure is not drawn to scale.)

  • A.

    3\sqrt{5}

  • B.

    10

  • C.

    6\sqrt{5}

  • D.

    20

  • E.

    25

Answer:D

A D=A P+P D=3+2=5 A B C D is a rhombus, so A B=A D=5. \triangle A P B is a 3-4-5 right triangle, hence B P=4. The area of the rhombus is base times height: b h=(A D)(B P)=5 \cdot 4=20.

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