quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR = 8. Find XY^2.

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15-02-2020
Mathematics

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quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR = 8. Find XY^2.

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cphill cphill · Answer 1 · 2020-02-16T01:18:46+01:00

cphill cphill

16-02-2020

We can drop a perpendicular from X to PQ at A, and from Y to RS at B. Then XA = YB = 48/10 = 24/5. We can also draw a line through X parallel to BY meeting the line through Y parallel to RS at C.

Then XC = 24/5 + 24/5 + 10 = 98/5 and YC = 10 - 34/5 = 16/5, so XY^2 = XC^2 + YC^2 = (98/5)^2 + (16/5)^2 = 1972/5.

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