Brain Teasers and Puzzles

A box for your workings out:

Hint: You might find Pythagoras' theorem very useful [a² + b² = c²].

Answer: 148 inches.

We can use Pythagoras' theorem if we draw an imaginary line across to create a right-angled 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:

   a² + b² = c²

Where c is the hypotenuse.

This gives us:

          48² + (R - 8)² = R²

   2304 + (R - 8)(R - 8) = R²

    2304 + R² - 16R + 64 = R²

         2304 - 16R + 64 = 0

                     16R = 2368

                       R = 148

As required.