The required expression for the area of the rectangle in terms of x, where x denotes a shorter side of the rectangle is [tex]A=2.5 \ x^{2}[/tex] and the area if x=32 feet, is [tex]2560 \ sq \ ft.[/tex]
Given, The shorter side is x.
Since The longer side is [tex]2.5[/tex] times the shorter side so,
Longer side will be [tex]2.5 x[/tex].
We have Area of rectangle,
[tex]A= length \times\ breadth[/tex]
So, [tex]A= x\times 2.5x[/tex]
Or,[tex]A=2.5 \ x^{2}[/tex]
Now we have to calculate the area when [tex]x=32 \ feet[/tex],
So, [tex]A=2.5\times (32)^{2}[/tex]
[tex]A=2.5\times 1024[/tex]
[tex]A=2560 \ sq \ ft[/tex].
Hence the required expression for the area of the rectangle in terms of x, where x denotes a shorter side of the rectangle is [tex]A=2.5 \ x^{2}[/tex] and the area if x=32 feet, is 2560 sq ft.
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