Question

You invent a game that is played on a perfect 12 foot by 12 foot square. What is the longest distance between any two points on the square? A. 12 feetB. 15 feetC. 17 feetD. None of the aboveI will really appreciate the help on this problem.

Answer 1

The given figure is a square that measures 12 foot by 12 foot. please see illustration below;

The square in the sketch above shows the longest distance between two opposite diagonals, and that is the hypotenuse, labelled as a.

In the triangle ADC, using Pythagoras' theorem;

`\begin{gathered} AD^2+DC^2=AC^2 \\ 12^2+12^2=a^2 \\ 144+144=a^2 \\ 288=a^2 \\ \sqrt[]{288}=a \\ a=16.97 \end{gathered}`

The longest distance which is a (that is AC) is approximately 17 ft as shown above (16.97 ft).