Question

Take a look at the streets in Phoenix. N 9th Avenue, N 10th Avenue, N 11th Avenue, N 12th Avenue, and N 13th Avenue are parallel, and they intersect W Roosevelt Street and Phoenix-Wickenburg Hwy. The distance between N 15th Ave. and N 13th Ave., represented by segment AB, is 530 feet along W Roosevelt St. The distances between N 13th Ave. and N 12th Ave. (segment BC), between N 12th Ave. and N 11th Ave. (segment CD), between N 11th Ave. and N 10th Ave. (segment DE) and between N 10th Ave. and N 9th Ave. (segment EF) are all the same, 340 feet. Now let's find some distances between these avenues along Phoenix-Wickenburg Hwy. (segment AL).

If the distance on Phoenix-Wickenburg Hwy between 13th Avenue and 11th Avenue, represented by segment GJ is approximately 1060 feet, how long is Phoenix-Wickenburg Hwy. between 13th Avenue and 15th Avenue (segment AG) to the nearest foot?

1652 feet

826 feet

340 feet

530 feet

Answer 1

it will be 530 or 826

Answer 2

The correct option is 2.

Explanation:

Let the distance on Phoenix-Wickenburg Hwy between 13th Avenue and 15th Avenue be AG = x.

From the given diagram it is clear that the distance on Phoenix-Wickenburg Hwy is represented by a straight line.

In triangle ABG and ADJ,

`\angle A=\angle A` (Reflexive property)

`\angle ABG=\angle ADJ` (Right angle)

By AA property of similarity,

`\triangle ABG\sim \triangle ADJ`

The corresponding sides of similar triangles are proportional.

`(AB)/(AD)=(AG)/(AJ)`

`(AB)/(AB+BC+CD)=(AG)/(AG+GJ)` (Segment addition postulate)

Substitute AB=530, BC=340, CD=340, AG=x and GJ=1060 in above equation.

`(530)/(530+340+340)=(x)/(x+1060)`

`(530)/(1210)=(x)/(x+1060)`

`(53)/(121)=(x)/(x+1060)`

On cross multiplication we get

`53(x+1060)=121x`

`53x+56180=121x`

Subtract 53x from both the sides.

`56180=121x-53x`

`56180=68x`

Divide both sides by 68.

`(56180)/(68)=x`

`826.17647=x`

`x\approx 826`

The distance on Phoenix-Wickenburg Hwy between 13th Avenue and 15th Avenue is 826 feet. Therefore the correct option is 2.