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

Question

3 years ago

7

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

B.120 mi

C.240 mi

D.300 mi

2 answers:

elena55 [62] · Answer 1 · 2022-05-23T16:54:14+03:00

4 0

The answer is C. Hope this helps!

Lapatulllka [165] · Answer 2 · 2022-05-23T19:15:53+03:00

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