Question

1. The diagram below models the layout at the county fair. Suppose the two triangles in the diagram aresimilar.100RefreshmenPetting Zoo112112Restroom140RidesParkEntrancea. How far is the park entrance from the rides? Show/explain your work to justify your solution process.

Answer 1

Since they are similar triangles, it means all three sides of one triangle is in proportion with the corresponding three sides of the other triangle.

a) To find the distance from the park entrance to the rides, we have:

`(140)/(112)=(x)/(100)`

Let's solve for x.

Cross multiply:

`\begin{gathered} 112x=140(100) \\ \\ 112x=14000 \end{gathered}`

Divide both sides by 112:

`\begin{gathered} (112x)/(112)=(14000)/(112) \\ \\ x=125 \end{gathered}`

Therefore, the distance from the park entrance to the rides is 125

b) Distance from the rides to the refreshment area.

To find the distance from the rides to the refreshment area, add the distance from rides to the restroom and the distance from the restroom to the refreshment area.

Where distance from the rides to the restroom = distance from 140 (it's an isosceles triangle)

Thus, we have:

Distance from the rides to the refreshment area = 140 + 112 = 252

ANSWER:

A) 125

B) 252