The square has a property of having all the sides equal. The rectangle on the other hand has its opposite sides equal. The larger side of the rectangle is called length and the smaller side is called breadth. The area of rectangle is the product of length and breadth i.e.
[tex]\rm Area\:of\:rectangle = Length\: \times Breadth[/tex]
The side of square for the given question is [tex]4\rm \: inches[/tex].
Calculation:
Let the side of square be [tex]\rm x[/tex]
Given:
Area of rectangle is 9 square inches.
Side of square is reduced by 3 and other side is enlarged by 5. Therefore, dimensions of the rectangle will be:
[tex]\rm Breadth = x - 3\\\\Length = x + 5[/tex]
[tex]\rm Area\:of\:rectangle = Length\: \times Breadth\\\\9 = (x + 5)(x -3)\\\\9 = x^2 + 5x -3x -15 \\\\9 = x^2 +2x - 15 \\\\0 = x^2 +2x-15-9\\\\0 = x^2+2x-24\\\\[/tex]
On factoring the equation:
[tex]\begin{aligned} \rm x^2 + 2x -24 &= 0\\\\x^2 + 6x - 4x - 24 &= 0\\\\x(x+6)-4(x+6) &= 0\\\\(x+6)(x-4)&=0\end[/tex]
On equating [tex]\rm (x +6)[/tex] and [tex](x-4)[/tex] with 0 we get:
[tex]x = -6\\\\x=4[/tex]
Since side of square cannot be negative, [tex]x = 4[/tex] is the only correct value.
Therefore the side of square is [tex]4 \:\rm inches[/tex].
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