Answer:
[tex](x-6)[/tex] meters
Step-by-step explanation:
We  have been given that the area of a rectangle is [tex]x^2-11x+30[/tex] square meters and a length of [tex](x-5)[/tex] meters.
Since the area of a rectangle is product of its width and length.
[tex]\text{Area of rectangle}=\text{Width of rectangle*Length of rectangle}[/tex]
We can find width of our rectangle by dividing area of rectangle by length of rectangle.
[tex]\text{Width of rectangle}=\frac{\text{Area of rectangle}}{\text{Length of rectangle}}[/tex]
Let us substitute our given values in above formula.
[tex]\text{Width of rectangle}=\frac{x^2-11x+30}{x-5}[/tex]
Let us factor out numerator by splitting the middle term.
[tex]\text{Width of rectangle}=\frac{x^2-6x-5x+30}{(x-5)}[/tex]
[tex]\text{Width of rectangle}=\frac{x(x-6)-5(x-6)}{(x-5)}[/tex]
[tex]\text{Width of rectangle}=\frac{(x-6)(x-5)}{(x-5)}[/tex]
Upon cancelling out x-5 from numerator and denominator we will get,
[tex]\text{Width of rectangle}=(x-6)[/tex]
Therefore, the expression [tex](x-6)[/tex] meters represents width of the rectangle.
