jmc

Question

Mario is constructing a square dart board. It will consist of a smaller square centered in a larger square. The smaller square measures 4 inches on each side. The ratio of the area of the smaller square to the area of the entire dart board is 49. How long is the side of the larger square?

Accepted Answer

The smaller square has area 4^2 = 16. Suppose the side of the larger square is s; then, its area is s^2. It follows that 16s^2 = 49, so cross-multiplying s^2 = 36. As s > 0, then s = 6.