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Distance to the Nearest Road

## Four roads form a square ACDE with side length s. A barn B is 5 miles from A, 8 miles from C, and 13 miles from D. What is the shortest distance from the barn to the nearest road?

Do you need to find the length of a side of the square?

Do you need to find the distance from the barn to the fourth corner of the square?

Hint

Hints/Solution

Comments:

Those with a lust for algebraic manipulation can pursue the problem using multiple Pythagorean relationships. . .

This problem has been published in various forms. One version is in the design of a jewel box with a gem to be mounted in the square lid of the jewel box 5 inches, 8 inches, and 13 inches from respective corners. Usually, algebraic solutions have been published.

Extensions/Variations:Could the distance of 13 be from E to B rather than from D to B? Different result?

Could B be located outside the square?

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