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

Answer:

350 yards

Step-by-step 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:

$\dfrac{AB}{AD}= \dfrac{BC}{CD}\\\dfrac{x}{700}= \dfrac{200}{400}\\ Cross multiply\\400x=200 \times 700\\x=(200 \times 700) \div 400\\x=350 yards$

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