Question

How far is the park entrance to the rides How far are the rides from the restroomsHow far are the rides from the refreshment area The diagram below models the layout at the country fair assume the two triangles in the diagram are similar.

Answer 1

Given two triangles are similar.

A)

We know that the corresponding sides of similar triangles are in proportion.

Let x be the distance between the park entrance and the rides.

we get the proportions as follows.

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

Multiplying both sides by 100, we get

`(140)/(112)*100=(x)/(100)*100`
`x=125\text{ yards}`

Hence the Park entrance is 125 yards from the rides.

B)

Let y be the distance between rides and restrooms.

Since the given triangles are similar, we get the following proportion.

`(140)/(112)=(y)/(112)`

Multiplying both sides by 112, we get

`(140)/(112)*112=(y)/(112)*112`
`y=140\text{ yards.}`

Hence the rides are 140 yards from the restrooms.

C)

the distance between refreshment area and rides =The distance between refreshment area and restrooms + the distance between rides and restrooms

The distance between the refreshment area and rides=112+140=252 yards.

Hence the rides are 252 yards from the refreshment area.