Answer:
The correct option is 2.
Step-by-step 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,
[tex]\angle A=\angle A[/tex] (Reflexive property)
[tex]\angle ABG=\angle ADJ[/tex] (Right angle)
By AA property of similarity,
[tex]\triangle ABG\sim \triangle ADJ[/tex]
The corresponding sides of similar triangles are proportional.
[tex]\frac{AB}{AD}=\frac{AG}{AJ}[/tex]
[tex]\frac{AB}{AB+BC+CD}=\frac{AG}{AG+GJ}[/tex] (Segment addition postulate)
Substitute AB=530, BC=340, CD=340, AG=x and GJ=1060 in above equation.
[tex]\frac{530}{530+340+340}=\frac{x}{x+1060}[/tex]
[tex]\frac{530}{1210}=\frac{x}{x+1060}[/tex]
[tex]\frac{53}{121}=\frac{x}{x+1060}[/tex]
On cross multiplication we get
[tex]53(x+1060)=121x[/tex]
[tex]53x+56180=121x[/tex]
Subtract 53x from both the sides.
[tex]56180=121x-53x[/tex]
[tex]56180=68x[/tex]
Divide both sides by 68.
[tex]\frac{56180}{68}=x[/tex]
[tex]826.17647=x[/tex]
[tex]x\approx 826[/tex]
The distance on Phoenix-Wickenburg Hwy between 13th Avenue and 15th Avenue is 826 feet. Therefore the correct option is 2.
