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

Answer:

482.8

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step 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,

$=\sqrt{(0-0)^2+(120-0)^2}+\sqrt{(140-0)^2+(100-120)^2}+\sqrt{(140-140)^2+(20-100)^2}+\sqrt{(0-140)^2+(20-0)^2}$

$=\sqrt{120^2}+\sqrt{19600+400}+\sqrt{0+80^2}+\sqrt{19600+400}$

$=120+100\sqrt{2}+80+100\sqrt{2}$

$=200+200\sqrt{2}$

$=482.842712475$

$\approx 482.8\text{ feet}$

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