Question

The rectangle below has an area of x^2-11x+30x ​2 ​​ −11x+30x, start superscript, 2, end superscript, minus, 11, x, plus, 30 square meters and a length of x-5x−5x, minus, 5 meters. what expression represents the width of the rectangle?

Answer 1

the answer is x - 6, have a nice day

Answer 2

`(x-6)` meters

Explanation:

We have been given that the area of a rectangle is
`x^2-11x+30` square meters and a length of
`(x-5)` meters.

Since the area of a rectangle is product of its width and length.

`\text{Area of rectangle}=\text{Width of rectangle*Length of rectangle}`

We can find width of our rectangle by dividing area of rectangle by length of rectangle.

`\text{Width of rectangle}=\frac{\text{Area of rectangle}}{\text{Length of rectangle}}`

Let us substitute our given values in above formula.

`\text{Width of rectangle}=(x^2-11x+30)/(x-5)`

Let us factor out numerator by splitting the middle term.

`\text{Width of rectangle}=(x^2-6x-5x+30)/((x-5))`

`\text{Width of rectangle}=(x(x-6)-5(x-6))/((x-5))`

`\text{Width of rectangle}=((x-6)(x-5))/((x-5))`

Upon cancelling out x-5 from numerator and denominator we will get,

`\text{Width of rectangle}=(x-6)`

Therefore, the expression
`(x-6)` meters represents width of the rectangle.