The width of the rectangles is 4.
Step-by-step explanation:
Given that two rectangles have same width. So, let be the two rectangles [tex]R_{1}[/tex] and [tex]R_{2}[/tex] and width of rectangle is ‘x’. So, according to question, we have
Length of one rectangle , [tex]R_{1}[/tex] = x + 1
Length of other rectangle, [tex]R_{2}[/tex] = x + 2
But we also know that,
[tex]\text { Area of rectangle } = \text { Length } \times \text { width }[/tex]
So, then the area for one rectangle,
[tex]\text { Area of rectangle } R_{1} = x \times(x+1)[/tex]
Similarly,
[tex]\text { Area of rectangle } R_{2} = x \times(x+2)[/tex]
So, according to question,
[tex]\text {Area of rectangle } R_{2} = 4 \times \text { Area of rectangle } R_{1}[/tex]
[tex]x \times(x+2) = 4+x \times(x+1)[/tex]
Now, by solving the above equation, we get
[tex]x^{2}+2 x = 4+x^{2}+x[/tex]
[tex]x = 4[/tex]
So, from the above equation, we found that width of the rectangle is 4.
