The dimensions of a rectangular-shaped garden are length is 28 feet and width is 15 feet.
A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
Let length of the garden be l and
Let width of the garden be w
Here [tex]l = 2w - 2[/tex].
Area of the rectangular-shaped garden = 420 square feet
The formula of area of the rectangle is
[tex]A=lw[/tex]
⇒ [tex]420=(2w-2)(w)[/tex]
⇒ [tex]420=w^{2} -2w[/tex]
⇒ [tex]w^{2} -2w-420=0[/tex]
⇒ [tex](w-15)(w+14)=0[/tex]
Then w can take values,
[tex]w=15[/tex] or [tex]w=-14[/tex]
The value of width always be positive value, so
[tex]w=15[/tex]
Now, [tex]l = 2(15) - 2[/tex]
⇒ [tex]l=30-2[/tex]
⇒ [tex]l=28[/tex]
Hence we can conclude that the dimensions of a rectangular-shaped garden are length is 28 feet and width is 15 feet.
Learn more about the rectangles here
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