Answer:
The student incorrectly simplified [tex]30ab\sqrt{2a}+20a\sqrt{2a}[/tex] .
Thus, option D is correct.
Step-by-step explanation:
The formula to determine the Perimeter of a rectangle of width w and length l is expressed as:
[tex]P = 2l + 2w[/tex]
In other words, the perimeter can be determined by multiplying the length and width by 2 and adding the result.
In our case, the dimensions of a rectangle are [tex]\sqrt{50a^3b^2}[/tex] and [tex]\sqrt{200a^3}\:\:[/tex].
Here is the student's solution:
[tex]2\sqrt{50a^3b^2}+2\sqrt{200a^3}=2\cdot 5ab\sqrt{2a}+2\cdot 10a\sqrt{2a}[/tex]
[tex]=10ab\sqrt{2a}+20a\sqrt{2a}[/tex]
[tex]=30ab\sqrt{2a}[/tex]
The student made an error in calculating [tex]30ab\sqrt{2a}+20a\sqrt{2a}[/tex] , because [tex]30ab\sqrt{2a}+20a\sqrt{2a}[/tex] are not like terms.
Hence, [tex]30ab\sqrt{2a}+20a\sqrt{2a}[/tex] can not be simplified to [tex]30ab\sqrt{2a}[/tex]
Therefore, the student incorrectly simplified [tex]30ab\sqrt{2a}+20a\sqrt{2a}[/tex] .
Thus, option D is correct.
Here is the correct Solution:
[tex]2\sqrt{50a^3b^2}+2\sqrt{200a^3}=2\cdot 5ab\sqrt{2a}+2\cdot 10a\sqrt{2a}[/tex]
[tex]=10ab\sqrt{2a}+20a\sqrt{2a}[/tex]
