Stack of Water Pipes

Three of the new water pipes for Main Street are stacked as shown. The external diameter of each pipe is 12 inches. How tall is the stack (h in the picture)?




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h = AB + BC + CD.

AB = 6 and CD = 6. Those are easy.

BC is the altitude of equilateral △BXY with sides of length 12.

XC = 6, △BXC is a 30 – 60 – 90 right △,
so BC = 6√3.

Thus h = 6 + 6√3 + 6 = 12 + 6√3.

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