The width of rectangle is 3 units.
Step-by-step explanation:
Given,
Area of rectangle = Perimeter of rectangle
Let,
width of rectangle = w
Length of rectangle = w+3
Area = Length*Width
Perimeter = 2(Length+Width)
It is given that;
Area of rectangle = Perimeter of rectangle
[tex]l*w=2(Length+Width)\\(w+3)w=2(w+3+w)\\w^2+3w=2(2w+3)\\w^2+3w=4w+6\\w^2+3w-4w-6=0\\w^2-w-6=0[/tex]
Factorizing the equation,
[tex]w^2-3w+2w-6=0\\w(w-3)+2(w-3)=0\\(w-3)(w+2)=0[/tex]
Either,
w-3=0 => w=3
Or,
w+2=0 => w= -2
As width cannot be negative, therefore,
The width of rectangle is 3 units.
Keywords: area, perimeter
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