Question

Randall purchased a plot of land for his business. The figure represents a plan of the land showing the location of the office space, parking lot and open space for a yard so that the employees and visitors can enjoy time outside. The coordinates represent points on a rectangular grid with units in feet. What is the perimeter of the plot of land rounded to the nearest tenth of a foot?

Answer 1

482.8

Explanation:

Answer 2

The perimeter of the plot of land is approximately 482.8 feets.

Explanation:

By the given diagram,

The perimeter of the plot of land = The perimeter of the quadrilateral having the vertices (0,0), (0,120), (140,100) and (140,20),

Since, the perimeter of the quadrilateral having the vertices (0,0), (0,120), (140,100) and (140,20) = The distance between (0,0) and (0,120) + The distance between (0,120) and (140,100) + The distance between (140,100) and (140,20) + The distance between (140,20) and (0,0)

By the distance formula,

`=√((0-0)^2+(120-0)^2)+√((140-0)^2+(100-120)^2)+√((140-140)^2+(20-100)^2)+√((0-140)^2+(20-0)^2)`

`=√(120^2)+√(19600+400)+√(0+80^2)+√(19600+400)`

`=120+100√(2)+80+100√(2)`

`=200+200√(2)`

`=482.842712475`

`\approx 482.8\text{ feet}`

Hence, the perimeter of the plot land is approximately 482.8 feets.