Question

ABCD is a rectangle that represents a park. The lines show all the paths in the park. The circular path is in the centre of the rectangle and has a diameter of 10 m. Calculate the shortest distance from A to C across the park, using only the lines shown. B 40 m A 70 m C D​

Answer 1

Answer is 86.3 m from A to C
This is using 3.14 for pi and rounded to tenths

Step by step

First we will find the diagonal by using Pythagorean theorem a^2 + b^2 = c^2

We know the a & b sides, looking for c the hypotenuse or diagonal

40^2 + 70^2 = c^2

1600 + 4900 = c^2

6500 = c^2

80.6 = c = the full diagonal length.

Now we know the circle has a diameter of 10, so we subtract that from the diagonal length.

80.6 - 10 = 70.6m

Now we need to find the circumference of the circle using C = 2 TT r

We know the diameter is 10, so radius is half of that, so r=5

C = (2) (3.14) (5)

C = 31.4

Since we walk only half of the circle to get from A to C, we divide our circumference by 2.

31.4 / 2 = 15.7

So we have diagonal length of 70.6 + half the circle 15.7 for a total of 86.3m for the path as highlighted on the attachment