Ahighway between points a and b has been closed for repairs. an alternative route between there two locations is to travel between a and c and then from c to b what is the value of y and what is the total distance from a to c to b?

The value of Y is 24 km and distance from A to C to B is AC+Y=18+24=42 km

Step-by-step explanation:

Given that A highway between points A and B has been closed for repairs. An alternative route between there two locations is to travel between A and C and then from C to B. we have to find the value of Y and the total distance from A to C to B. Let AB=Z

In ΔBCD and ΔABD

∠BCD=∠ABD       (∵each 90°)

∠D=∠D                 (∵common)

By AA similarity, ΔBCD~ΔABD

∴ their corresponding sides are proportional

Comparing last two terms, we get

⇒

⇒

⇒

⇒

⇒

Hence, the roots are X=32, -50

X=-50 not possible as distance can never negative.

Hence, X=32 km

By applying Pythagoras theorem in ΔBCD we get

⇒

⇒

Hence, the value of Y is 24 km and the distance from A to C to B is AC+Y=18+24=42 km

step-by-step explanation:

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