Question

PROBLEM SOLVING

21. CITY MAP On the map below, Idaho Avenue bisects the angle between


University Avenue and Walter Street. To the nearest yard, what is the distance


along University Avenue from 12th Street to Washington Street?


12th St


University Ave


700 yd


Walter St


Idaho Ave


200 yd


400 yd


Washington St

Answer 1

350 yards

Explanation:

Angle bisector theorem: The angle bisector of a triangle divides opposite sides proportionally.

We use the angle bisector theorem to find the value of x in the diagram.

Therefore:

`(AB)/(AD)= (BC)/(CD)\\(x)/(700)= (200)/(400)\\$Cross multiply\\400x=200 * 700\\x=(200 * 700) / 400\\x=350$ yards`

Therefore, the distance along University Avenue from 12th Street to Washington Street is 350 yards.