If the area is x^2+5x+6m^2 and we know the area is a square which is base times height, we can factor the equation so that it comes out to (x+3)(x+2)since the height is x+3 then we know the base is x+2. (is this correct)

your figure cannot be a square, since the base and the height is not the same.

your math is correct, since
(x+3)(x+2) = x^2+5x+6 (I assumed the 6m^2 was a typo)

are you sure it did not say 'rectangle' ?

Thank you!!

Yes, your understanding is correct. To factor the quadratic expression x^2 + 5x + 6, you need to find two numbers that multiply to 6 and add up to 5 (since the coefficient of x is positive). Those numbers are 2 and 3. So, you can rewrite the expression as (x + 3)(x + 2).

Now, let's consider the area of the square. The area is given by the product of the base and the height. In this case, since the base is x + 2 and the height is x + 3, the area can be written as (x + 2)(x + 3) or (x + 3)(x + 2), which are equivalent.

Therefore, your conclusion that the base is x + 2 and the height is x + 3 is correct based on the given expression and the fact that the area is a square.