

Explanation
(a) By the use of Pythagoras theorem, the hypotenuse side is 13 and also sin x = \(\frac{5}{13}\) andcos x = \(\frac{12}{13}\) Substituting and simplifying yields \(\frac{65}{161}\)
(b)we have (11 + 2x)(14 + 2x) -(11 x 14) =186.
Expanding and simplifying to get the quadratic equation 2x\(^2\) +25x -93 = 0.
Solving the quadratic equation results in x = 3 m as the width of the path.

