The required value of the width is [tex]\frac{5}{2} cm[/tex]
Given,
The area of the square is 375cm.
Length of the rectangle=30 cm
The breadth of the rectangle=20cm
The formula for the area of the square is,
[tex]Area=l\times b[/tex]
The inside length =30-2x
Inside breadth=20-2x
Then,
[tex](30-2x)(20-2x)=375\\600-100x+4x^2=375\\(2x-45)(2x-5)=0\\x=\frac{45}{2} ,\frac{5}{2}[/tex]
So, [tex]x=\frac{5}{2}[/tex] as [tex]x\neq \frac{45}{2}[/tex]
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