FILE No.99Unsolved
A hidden room in a cellar is 3 m wide and 4 m long. A suspect says, "From corner to opposite corner, the diagonal was about 6 m."
Police know that in a right triangle, the long side is the square root of the sum of the squares of the other two sides.
What is the real diagonal of the room?
If you get stuck, open the hints one at a time, in order.
What triangle does the diagonal form?
Square the width and the length, then add.
Take the square root.
What is the real diagonal of the room?
Choose the answer closest to the truth.
5 m
The answer is: 5 m.
The diagonal splits the rectangle into right triangles. The diagonal is the square root of (3 x 3 + 4 x 4) = the square root of (9 + 16) = the square root of 25 = 5.
3, 4, 5 is a famous right triangle. The suspect's "6 m" is a full metre too long, so he may never have been in the room.
Without calculating, "shorter than 3 + 4 = 7" still does not give the exact length.
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