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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 what is the value of Y and what is the total distance from A to C to B?

A highway between points A and B has been closed for repairs. An alternative route-example-1
User Hilsenrat
by
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1 Answer

4 votes

Answer:

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

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


(Y)/(Z)=(X)/(40)=(40)/(18+X)

Comparing last two terms, we get


(X)/(40)=(40)/(18+x)


X(18+X)=1600


18X+X^2=1600


X^2+18X-1600=0


X^2-32X+50X-1600=0


(X-32)(X+50)=0

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


BD^2=BC^2+CD^2


40^2=Y^2+32^2


Y^2=1600-1024=576


Y=\sqrt576=24km

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




User Barlas Apaydin
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