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The map below shows the street locations of a city. Position three police officers such that the entire length of every street can be seen by at least one officer.
The middle of the triangle contains the square root of the sum of the three surrounding numbers.
Puzzle 403
After visiting my Great Aunt Anne, I travelled home in her old jalopy. The car was old and battered, it had a leak from the petrol tank, and I was stuck in second gear.
This meant that I could only travel along at a steady 30 miles per hour and managed a paltry 20 miles per gallon of fuel.
At the start of the journey I had placed exactly 10 gallons of fuel into the tank. I knew though, that the fuel tank lost fuel at the rate of half a gallon per hour.
Just as I arrived home, the car stopped because it had run out of fuel and I had only just made it.
Hint: You might find Pythagoras' theorem very useful [a^{2} + b^{2} = c^{2}].
Answer: 148 inches.
We can use Pythagoras' theorem if we draw an imaginary line across to create a rightangled triangle.
The hypotenuse is equal to the rope's length R. The bottom of the triangle is 48 inches. The vertical side is R  8 (the difference between 20 inches and 12 inches).
Pythagoras' theorem tells us that:
a^{2} + b^{2} = c^{2}
Where c is the hypotenuse.
This gives us:
48^{2} + (R  8)^{2} = R^{2}
^{ }^{ } 2304 + (R  8)(R  8) = R^{2}
^{ } 2304 + R^{2}  16R + 64 = R^{2}
^{ }^{ } 2304  16R + 64 = 0
^{ }^{ } 16R = 2368
^{ }^{ } R = 148
As required.
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