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The length of a rectangle is 12 ft longer than twice the width. If the perimeter is 96 ft, find the length and width of the rectangle

Sagot :

Let the length of the rectangle = L

Width of the rectangle = w

The length of a rectangle is 12 ft longer than twice the width.

So,

[tex]l=12+2w[/tex]

The perimeter of the rectangle is given by the formula:

[tex]P=2(l+w)[/tex]

Given perimeter = 96 ft

Substitute with the perimeter and the equation of the length into the equation of the perimeter

So,

[tex]2(12+2w+w)=96[/tex]

Solve the equation to find w:

[tex]\begin{gathered} 12+3w=\frac{96}{2} \\ 3w+12=48 \\ 3w=48-12 \\ 3w=36 \\ w=\frac{36}{3}=12 \end{gathered}[/tex]

So, the length of the rectangle =

[tex]l=12+2w=12+24=36[/tex]

So, the answer will be:

Length = 36 ft

Width = 12 ft

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