The area of a rectangle is found by multiplying the length by the width: A=lw. A certain rectangle has an area os x^2+7x +12. Factor the trinomial to find the length ad width of the rectagle.

Please read at this site:
http://www.themathpage.com/alg/factoring-trinomials.htm

Then see if the below makes sense.

(x+3) (x+4)

Three girls paid $100 each, a total of $300, to share a Motel Room. Later, the desk clerk realizing she should have only charged $250, gives the Room Attendant $50 and asks him to return it to the three girls. Unable to divide the money three ways, he decides to give $10 to each girl and pockets the remaining $20. The girls have now paid $90 each or $270 for the room, and the room attendant has $20. What happened to the other $10?

There is no other $10. The total was $300, the girls got back $10 each, meaning they paid $270 for the room, and the other guy took the last $20, will adds up to the entire $50 refund. The original $300 is all accounted for. $250 is in the cash register. $30 is with the 3 girls, and $20 is with the clerk.

The given trinomial can be factored as follows:

x^2 + 7x + 12 = (x + 3)(x + 4)

Therefore, the factors of the trinomial are (x + 3) and (x + 4).

Now, let's relate this to finding the length and width of the rectangle. We know that the area of a rectangle is given by the formula A = l * w, where A represents the area, l represents the length, and w represents the width.

Since we have the trinomial x^2 + 7x + 12, we can equate it to the area of the rectangle.

x^2 + 7x + 12 = l * w

Now, by factoring the trinomial as (x + 3)(x + 4), we can replace the trinomial with the factors in the equation:

(x + 3)(x + 4) = l * w

This means that the length (l) of the rectangle is (x + 3), and the width (w) of the rectangle is (x + 4).

Thus, the length and width of the rectangle are (x + 3) and (x + 4), respectively.

To factor the trinomial x^2 + 7x + 12 to find the length and width of the rectangle, we can follow the steps:

Step 1: Look for two binomials in the form (x + ?) and (x + ?) that when multiplied together, will give us the given trinomial.

Step 2: The first terms of the two binomials should have a product of x^2.

Step 3: The last terms of the two binomials should have a product of 12.

Step 4: The middle term of the trinomial (7x) can be factored into the sum or difference of the two numbers obtained in the previous steps.

Looking at the trinomial x^2 + 7x + 12, we can find two numbers whose product is 12 and whose sum is 7. The numbers are 3 and 4.

So, using the numbers 3 and 4, we can factor the trinomial as follows:

(x + 3) (x + 4)

In this case, the length of the rectangle would be (x + 3) and the width would be (x + 4).

I have read the content provided in the website you mentioned, and it appears to be a helpful resource for understanding how to factor trinomials.