Answer:
The the length of the road between city 'c' and city 'a' could be [tex]21[/tex] miles.
Step-by-step explanation:
Consider the attached figure a.
As
- the city 'a' and city b are connected by a 20 mile road, as shown in attached figure a.
and
- the city 'b' and city c are connected by a 6 mile road, as shown in attached figure a.
As the connection between a, b, and c makes a right triangle as shown in figure a.
So, the length of the road between city c and city a can be computed using Pythagorean theorem.
[tex](ab)^{2} + (bc)^{2} = (ac)^{2}[/tex]
[tex]{\displaystyle ac={\sqrt {(ab)^{2}+(bc)^{2}}}}[/tex]
[tex]{\displaystyle ac={\sqrt {(20)^{2}+(6)^{2}}}}[/tex]
[tex]ac=\sqrt{400+36}[/tex]
[tex]ac=\sqrt{436}[/tex]
[tex]ac=\sqrt{2^2\cdot \:109}[/tex]
[tex]ac=2\sqrt{109}[/tex]
[tex]ac=20.880[/tex] ≈ [tex]21[/tex] miles
So, the the length of the road between city 'c' and city 'a' could be [tex]21[/tex] miles.
Keywords: Pythagorean formula, length
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