Question

Two city streets are

parallel. The measurements between the
streets and a landmark are shown in the
figure. Find the distance between 1st Street
and 2nd Street along Pike Avenue and the
distance between 2nd Street and the
landmark along Pike Avenue.

Answer 1

1.456341245959493929293&3&3838

Answer 2

• The distance between 1st Street and 2nd Street along Pike Avenue is 60 ft.
• The distance between 2nd Street and the landmark along Pike Avenue i 240 ft.

Explanation:

Similar Triangles - Side Splitter Theorem

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Let x be the distance between 1st Street and 2nd Street along Pike Avenue.

As 1st Street and 2nd Street are parallel we can use the Side Splitter Theorem to calculate x:

`\implies \sf x:300=40:40+160`

`\implies \sf x:300=40:200`

`\implies \sf (x)/(300)=(40)/(200)`

`\implies \sf x=(40)/(200) \cdot 300`

`\implies \sf x=60\; ft`

To calculate the distance between 2nd Street and the landmark along Pike Avenue, subtract the found distance between 1st Street and 2nd Street along Pike Avenue from the length of Pike Avenue:

`\implies \sf 300-60=240\; ft`