The dimensions of the rectangle are length is 6 yd and width is 11/2 yd.
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. The dimensions of rectangle are length and width.
For the given situation,
Let l be the length of the rectangle and
Let w be the width of the rectangle
The length of the rectangle is 5 yd less than twice the width,
[tex]l=2w-5[/tex]
The area of a rectangle = 33 yd^2
The formula for area of rectangle is
[tex]A=lw[/tex]
⇒ [tex]33=(2w-5)(w)[/tex]
⇒ [tex]33=2w^{2} -5w[/tex]
⇒ [tex]2w^{2} -5w-33=0[/tex]
This equation can be factored as
⇒ [tex]2w^{2} +6w-11w-33=0[/tex]
⇒ [tex]2w(w+3)-11(w+3)=0[/tex]
⇒ [tex](2w-11)(w+3)=0[/tex]
⇒ [tex]2w-11=0[/tex] or [tex]w+3=0[/tex]
⇒ [tex]w=\frac{11}{2}[/tex] or [tex]w=-3[/tex]
Dimension cannot be negative. So we take width as w = 11/2.
Now, length is
⇒ [tex]l=2(\frac{11}{2} )-5[/tex]
⇒ [tex]l=11-5[/tex]
⇒ [tex]l=6[/tex]
Hence we can conclude that the dimensions of the rectangle are length is 6 yd and width is 11/2 yd.
Learn more about the rectangles here
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