Question

Two rectangles have the same width. The length of one is 1 foot longer than the width.

Answer 1

The width of the rectangles is 4.

Step-by-step explanation:

Given that two rectangles have same width. So, let be the two rectangles $R_{1}$ and $R_{2}$ and width of rectangle is ‘x’. So, according to question, we have  

Length of one rectangle , $R_{1}$ = x + 1

Length of other rectangle, $R_{2}$ = x + 2

But we also know that,

                  $\text { Area of rectangle } = \text { Length } \times \text { width }$

So,  then the area for one rectangle,

                $\text { Area of rectangle } R_{1} = x \times(x+1)$

Similarly,

                $\text { Area of rectangle } R_{2} = x \times(x+2)$

So, according to question,

                $\text {Area of rectangle } R_{2} = 4 \times \text { Area of rectangle } R_{1}$

                $x \times(x+2) = 4+x \times(x+1)$

Now, by solving the above equation, we get

                $x^{2}+2 x = 4+x^{2}+x$

                $x = 4$

So, from the above equation, we found that width of the rectangle is 4.