For Chap 13, Lesson 6, #32, the basis for the answers is the figure for #6. If we look carefully at the grid, applying the Pythagorean Theorem gives XY^2 = 2^2 + 2^2 = 8, so XY = sqrt8 = 2sqrt2. YZ^2 = 1^2 + 1^2 = 2, so YZ =sqrt2. Therefore XY = 2YZ.

Harold Jacobs

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