Question

Study the road plan shown in the figure. A service station will be built on the highway, and a road will connect it with Cray. How long will the new road be?
A.180 mi


B.120 mi


C.240 mi


D.300 mi

Answer 1

The answer is C. Hope this helps! 

Answer 2

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

$\frac{AB}{BD}=\frac{AC}{BC}\\\\\Rightarrow\ \frac{400}{x}=\frac{500}{300}\\\\\Rightarrow\ x=\frac{3\times400}{5}\\\\\Rightarrow\ x=240\ mi$

Hence, The length of new road = 240 mi