Length and width of a given rectangle is equals to [tex]12[/tex] feet and [tex]8[/tex] feet respectively.
What is rectangle?
" Rectangle is defined as the quadrilateral whose opposite side are congruent and parallel to each other , each interior angle is of measure [tex]90[/tex] degrees."
Formula used
Perimeter of a rectangle [tex]= 2 ( length + width)[/tex]
According to the question,
Given,
Perimeter of a rectangle [tex]= 40[/tex] feet
Ratio of the width to the length [tex]=\frac{2}{3}[/tex]
[tex]'x'[/tex] represent the length of the rectangle
[tex]\frac{2x}{3}[/tex] represents the width of the rectangle
Substitute the values in the formula we get,
[tex]2( x+ \frac{2x}{3}) = 40\\\\\implies \frac{3x+2x}{3} =20\\\\\implies \frac{5x}{3} = 20\\\\\implies x = 12[/tex]
Length [tex]= 12[/tex] feet
Width [tex]= \frac{2(12)}{3}[/tex]
[tex]= 8[/tex] feet
Hence, length and width of a given rectangle is equals to [tex]12[/tex] feet and [tex]8[/tex] feet respectively.
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