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Novay_Z [31]
2 years ago
7

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. H

ow long will the new road be?
A.180 mi


B.120 mi


C.240 mi


D.300 mi

Mathematics
2 answers:
elena55 [62]2 years ago
4 0
The answer is C. Hope this helps! 
Lapatulllka [165]2 years ago
3 0

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

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