The maximum distance between the base of pole A and the base of pole B is 8 ft.
Height of the building A =3 ft
Height of the building B =7 ft
Length of the rope = 9 ft
Suppose the maximum distance between the base of pole A and the base of pole B is x ft.
Find the attached diagram to visualize the given situation better.
What is Pythagoras' theorem?
The square on the hypotenuse is equal to the sum of the squares on the other two sides.
Using the Pythagoras' theorem
[tex]9^{2} =4^{2} +x^{2}[/tex]
[tex]x^{2} =9^{2} -4^{2}[/tex]
[tex]x^{2} =81-16[/tex]
[tex]x=\sqrt{65}[/tex]
x ≈8 ft.
Therefore, the maximum distance between the base of pole A and the base of pole B is 8 ft.
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