Question

The dimensions of a rectangle are √50a^3b^2 and √200a^3. What is the students error?

Answer 1

Answer:

The student incorrectly simplified $30ab\sqrt{2a}+20a\sqrt{2a}$ .

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:

$P = 2l + 2w$

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 $\sqrt{50a^3b^2}$  and  $\sqrt{200a^3}\:\:$.

Here is the student's solution:

$2\sqrt{50a^3b^2}+2\sqrt{200a^3}=2\cdot 5ab\sqrt{2a}+2\cdot 10a\sqrt{2a}$

                                 $=10ab\sqrt{2a}+20a\sqrt{2a}$

                                 $=30ab\sqrt{2a}$          

The student made an error in calculating $30ab\sqrt{2a}+20a\sqrt{2a}$ , because $30ab\sqrt{2a}+20a\sqrt{2a}$ are not like terms.

Hence, $30ab\sqrt{2a}+20a\sqrt{2a}$ can not be simplified to $30ab\sqrt{2a}$

Therefore, the student incorrectly simplified $30ab\sqrt{2a}+20a\sqrt{2a}$ .

Thus, option D is correct.

Here is the correct Solution:

$2\sqrt{50a^3b^2}+2\sqrt{200a^3}=2\cdot 5ab\sqrt{2a}+2\cdot 10a\sqrt{2a}$

                                 $=10ab\sqrt{2a}+20a\sqrt{2a}$

Answer 2

Answer: D

Step-by-step explanation

got it right on edg