Answer: C.240 mi
Step-by-step explanation:
In the given picture, Let ABC be the bigger triangle and BDC be the smaller triangle.
Then, In ΔABC and ΔBDC
∠C=∠C
∠D=∠B =90°
Therefore, ΔABC ≈ ΔBDC [By AA similarity rule]
We know that the sides of similar triangles are proportional, then
[tex]\frac{AB}{BD}=\frac{AC}{BC}\\\\\Rightarrow\ \frac{400}{x}=\frac{500}{300}\\\\\Rightarrow\ x=\frac{3\times400}{5}\\\\\Rightarrow\ x=240\ mi[/tex]
Hence, The length of new road = 240 mi
