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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 15 m.
Calculate the shortest distance from A to C
across the park, using only the lines shown.
50 m
80 m

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 1 class=

Respuesta :

calculista

Answer:

The shortest distance from A to C is 102.89 meters

Step-by-step explanation:

step 1

Possibility N 1

The distance from A to C is equal to the length side AD plus the length side DC

so

[tex]d_1=AD+DC=80+50=130\ m[/tex]

step 2

Possibility 2

The distance from A to C is equal to the diagonal AC minus the diameter of the circle plus the semi-circumference of the circle

Find the diagonal AC

Applying the Pythagorean Theorem

[tex]AC^2=80^2+50^2\\AC^2=8,900\\AC=94.34\ m[/tex]

Find the semi-circumference of the circle

[tex]C=\frac{1}{2}\pi D[/tex]

we have

[tex]D=15\ m\\\pi=3.14[/tex]

substitute

[tex]C=\frac{1}{2}(3.14)(15)=23.55\ m[/tex]

The distance  2 is equal to

[tex]94.34-15+23.55=102.89\ m[/tex]

therefore

The shortest distance from A to C is 102.89 meters

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