hello
to solve this question, we have to understand that a soccer field is rectangular in shape and we can find this length from factoring the area
formula of area of a rectangle
[tex]\begin{gathered} A=L\times W \\ A=\text{area} \\ L=\text{length} \\ W=\text{width} \end{gathered}[/tex][tex]\begin{gathered} A=24x^2+100x+100 \\ W=4x+10 \\ L=\text{ ?} \end{gathered}[/tex]
we can proceed to solve this by dividing the polynomial or simply checking it from the options
from the options given,
we have option A
3x + 10
let's multiply both the L and W to see if it gives us the answer
[tex](4x+10)\times(3x+10)=12x^2+70x+100_{}[/tex]
option A is incorrect
let's test for option B
L= 6x + 10
[tex]\begin{gathered} A=L\times W \\ (6x+10)\times(4x+10)=24x^2+100x+100_{} \end{gathered}[/tex]
option B is correct
let's test for option C
L= 6x + 1
[tex]\begin{gathered} A=L\times W \\ (6x+1)\times(4x+10)=24x^2+70x+10 \end{gathered}[/tex]
option C is also incorrect and so it'll be for option D
from the calculations above, only option B corresponds with the value of length for the soccer field
