Answer:
[tex]x+1[/tex] meters.
Step-by-step explanation:
Let L be the length of rectangle.
We have been given that the rectangle has an area of [tex]x^{2}-6x-7[/tex] square meters and a width of [tex]x-7[/tex] meters.
Since we know that area of rectangle is the product of its length and width.
[tex]\text{Area of rectangle}=\text{Width* Length}[/tex]
[tex]\text{ Length}=\frac{\text{Area of rectangle}}{\text{Width}}[/tex]
To find the length of our given rectangle we will divide area of rectangle by width of our rectangle.
[tex]L=\frac{x^2-6x-7}{x-7}[/tex]
Let us factor out our numerator by splitting the middle term.
[tex]L=\frac{x^2-7x+x-7}{x-7}[/tex]
[tex]L=\frac{x(x-7)+1(x-7)}{x-7}[/tex]
[tex]L=\frac{(x-7)(x+1)}{x-7}[/tex]
Upon cancelling out x-7 from numerator and denominator we will get,
[tex]L=(x+1)[/tex]
Therefore, the length of our rectangle will be [tex]x+1[/tex] meters.
