SOLUTION: To determine the width of a chasm, a marker (A) is placed directly opposite a rock (R) on the other side. Point B is placed 3 m away from point A, as shown. Marker C is placed 3 m

Algebra ->  Triangles -> SOLUTION: To determine the width of a chasm, a marker (A) is placed directly opposite a rock (R) on the other side. Point B is placed 3 m away from point A, as shown. Marker C is placed 3 m       Log On


   

Question 1044773: To determine the width of a chasm, a marker (A) is placed directly opposite a rock (R) on the other side. Point B is placed 3 m away from point A, as shown. Marker C is placed 3 m along the edge of the chasm, and marker D is placed so that BD is parallel to AC. Markers C and D and the rock are collinear (i.e. lie in a straight line). If BD measures 5 m, find the width of the chasm (AR).
http://imgur.com/a/UAxTy
Please show all working. Thank you!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
triangles BDR and ACR are similar; so, corresponding sides are proportional
than we have:
BD%2FAC=BR%2FAR......since BD=5m is parallel to AC=3m, and BR=3m%2BAR we will have

5m%2F3m=%283m%2BAR%29%2FAR

5cross%28m%29%2F3cross%28m%29=%283m%2BAR%29%2FAR

5%2F3=%283m%2BAR%29%2FAR

5%2AAR=%283m%2BAR%29%2A3

5%2AAR=9m%2B3%2AAR

5%2AAR-3%2AAR=9m

2%2AAR=9m

AR=9m%2F2

AR=4.5m