Answer:
12ab^3
Step-by-step explanation:
Given that:
Area of rectangle = 72a^3b^4
Width of rectangle = 6a^2b
Area = Length * Width
Length = Area / Width
Length = 72a^3b^4 / 6a^2b
Length = 72 / 6 * a^3 / a^2 * b^4 / b
Length = 12 * a * b^3
Length = 12ab^3
The required length is [tex]l=12ab^3[/tex].
The area of a rectangle is the region covered by the rectangle in a two-dimensional plane. A rectangle is a type of quadrilateral and the formula is,
[tex]A=l \times b[/tex]
Given that,
[tex]Area=72a^3b^4\\width=6a^2b[/tex]
Now, applying the above formula for finding the length of the rectangle,
[tex]Area=l\times b\\72a^3b^4= l \times 6a^2b[/tex]
Now, do the cross multiplication into the obtained equation.
[tex]\l=\frac{72a^3b^4}{ 6a^2b} \\l=12ab^3[/tex]
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