Your making a mosaic design on a square table top. You have already covered half of the table top with 150 1-inch square tile pieces. a. What are the dimensions of the table top? b. What is the measure of the diagonal from one corner to the opposite corner of the table top?

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Your making a mosaic design on a square table top. You have already covered half of the table top with 150 1-inch square tile pieces. a. What are the dimensions of the table top? b. What is the measure of the diagonal from one corner to the opposite corner of the table top?

Mathematics
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a) \[\sqrt{300} = 10\sqrt{3}\] b) \[10 \sqrt{6}\]
the steps are: we know that 150 1" tiles covers 1/2 the table, so the table's area must be 300 square inches. We also know the table is square (width and length are equal). We also know that L x W = AREA and if L and W are equal we can say they both equal L and that if AREA = L x W = L x L = L^2, then AREA = L^2 and L = sqrt(AREA). So...SQRT(300) = 10*sqrt(3) which is the answer to a) for b) we just use the Pythagorean Theorem (in a right triangle, the sum of the squares of the sides equals the square of the hypotenuse): \[(\sqrt{300})^{2} + (\sqrt{300})^{2} = 600\] and then take the square root of that:\[\sqrt{600} = 10\sqrt{6}\] (this is the distance from corner to corner)
Thank you johncroc :]

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