Respuesta :
The perimeter of the land that Tony will fence around the rectangular piece of land that he owns is 56 meters.
What is the perimeter of a rectangle?
The measure of the boundary of the sides of a rectangles called its perimeter. The perimeter of a rectangle is twice the sum its length and width.
[tex]P=2(l+w)[/tex]
Here, (l) is the length of the rectangle and (w) is the width of the rectangle.
The land has an area of 192 m2 and the length is 4m longer than the width. Let suppose the length is l. Thus,
[tex]l=4+w[/tex]
Now the area of rectangle is the product of length and width. Thus,
[tex]A=l\times w\\192=(4+w)\times w\\192=4w+w^2\\w^2+4w-192=0\\w^2+16w-12w-192=0\\w(w+16)-12(w+16)=0\\(w+16)(w-12)=0\\w=-16,12[/tex]
Taking positive side, w=12. The width of the rectangle is 12 m. The length of the rectangle is 4 m longer than the width. Thus, the length of it si 16 m (12+4). Its, perimeter is,
[tex]P=2(16+12)\\P=56\rm\;m[/tex]
Thus, the perimeter of the land that Tony will fence around the rectangular piece of land that he owns is 56 meters.
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