Question

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Answer 1

Answer:

The shortest walking route is through the diagonal AC: 102.89m

Step-by-step explanation:

One can go from A to C using 2 paths:

- ADC or ABC

- using diagonal AC and half of that inner circle.

We need to compute the length of each path.

1) ADC=AD+DC=80+50=130m

2) AC²=AD²+DC²=80²+50⁵=6400+2500= 8900m²

AC=sqrt(8900)=94.34m.

Note that the diagonal AC has a missing segment, whose length is the diameter of the inner circle. So the straight line has a length of: AC-d=94.34-15=79.34m.

Perimeter of half the circle=pi×r= 3.14×(15/2)= 3.14×7.5=23.55m

So, if one is using the diagonal to go from A to C, then he has to walk:

79.34+23.55=102.89m

Comparing the two routes: 130m vs 102.89m, we notice that the route using the diagonal AC is shorter.