Two rectangles have the same width. The length of one is 1 foot longer than the width.The length of the other is 2 feet longer than the width. The larger rectangle has 4 moresquare feet than the smaller. What is the width of the rectangles?

Accepted Solution

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 + 1Length of other rectangle, [tex]R_{2}[/tex] = x + 2But 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.