10. A rectangular field is $67 \mathrm{~m}$ long and $32 \mathrm{~m}$ wide. How much shorter (to the nearest tenth of a metre) is the distance from $A$ to $C$ than the distance from $A$ to $B$ to $C$ ?

Step 1 ：Given a rectangular field with length 67 m and width 32 m.

Step 2 ：The distance from A to C is the diagonal of the rectangle, which can be calculated using the Pythagorean theorem: \(\sqrt{67^2 + 32^2} \approx 74.2 \) m.

Step 3 ：The distance from A to B to C is simply the sum of the lengths of the two sides of the rectangle: \(67 + 32 = 99\) m.

Step 4 ：The difference between these two distances is the answer to the question: \(99 - 74.2 = 24.8\) m.

Step 5 ：Final Answer: The distance from A to C is \(\boxed{24.8}\) m shorter than the distance from A to B to C.