The length of the rectangle is [tex](6x+10)\text{ m}[/tex].
Important information:
- Area of a field = [tex](24x^2+100x+100)\text{ m}^2[/tex]
- Width = [tex](4x+10)\text{ m}[/tex]
We need to find the length.
Area of the rectangle:
We know that area of a rectangle is the product of its length and width.
[tex]A=l\times w[/tex]
The area expression can be written as:
[tex]A=24x^2+100x+100[/tex]
[tex]A=24x^2+60x+40x+100[/tex]
[tex]A=6x(4x+10)+10(4x+10)[/tex]
[tex]A=(6x+10)(4x+10)[/tex]
It is given that width = [tex](4x+10)\text{ m}[/tex].
Thus, the length of the rectangle is [tex](6x+10)\text{ m}[/tex].
Find out more about 'Area of the rectangle' here:
https://brainly.com/question/14383947
