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MathNet 2000 — Math Olympiad Vault Question 118

Math Olympiad Vault · MathNet 2000 — Math Olympiad Vault

Question 118

The canvas of a rectangular painting is surrounded by a mat, a border $10\ \mathrm{cm}$ wide. Outside the mat is a frame, also $10\ \mathrm{cm}$ wide. In the figure, the white rectangle is the canvas, the hatched region is the mat, and the black region is the frame.
The area of the whole picture, including the frame, is twice the combined area of the mat and canvas.
Question illustration
One can conclude that:
(A) The areas of the frame, mat, and canvas are all determined
(B) Only the frame area is determined
(C) Only the mat area is determined
(D) Only the canvas area is determined
(E) None of these areas is determined.