SOLUTION: A large pipe is placed next to a wall and a 1 ft high block is placed 5 ft from the wall to keep the pipe in place as show in the figure. What is the radius of the pipe ? The answe

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Extend a line from the top of the block to the vertical line thru the center of the pipe.
You get a right triangle with r as the hypotenuse.

If you solve that you'll get 6 ± sqrt(10)
6 - sqrt(10) is the answer.
6 + sqrt(10) puts the block on the other side of the pipe, between the pipe and the wall.
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btw, that's not a "large" pipe, less than 3 ft OD.

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You can find the triangle with the green leg since the triangle is a right triangle with the other leg and hypotenuse of .

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Substituting,



Complete the square,




Since , then must be less than .
So,