Question

Draw two rectangles.The first has length 6 and width 9. The second has length 3x and width 9. Write at least three different expressions for the sum of the areas of the rectangles.

Answer 1

Answer:

$A = 54 +27x$ (1)

And using factorization  (common factor) we can do this:

$A = 6*9 +9*3x = 9(6+3x)$ (2)

$A = 6*3*3 +9*3x = 3(18+9x)$ (3)

Step-by-step explanation:

In the figure attached we see the two triangles required one with a length of 6 and a width of 9 and the other with a length of 3x and width of 9.

For the first rectangle we know that the area can be founded with this formula:

$A_1 = bh = 6*9=54$

And for the second rectangle the area can be founded similar like this:

$A_2 = 9*3x = 27x$

And since we are interested in the sum of the two areas we have this:

$A = A_1 +A_2$

We need a 3 different expression for the sum of the areas so we can do this:

$A = 54 +27x$ (1)

And using factorization (common factor)  we can do this:

$A = 6*9 +9*3x = 9(6+3x)$ (2)

$A = 6*3*3 +9*3x = 3(18+9x)$ (3)