Question

Complete the explanation of how the figure illustrates that 6(9) = 6(4) + 6(5).

The area is the product of the length and width (6 × ? ). It is also the sum of the areas of the rectangles separated by the dished line (6 × ? and 6 × 5).
So, 6(9) = 6(4) + 6(5).

Answer 1

Answer:

The explanation of how the figure illustrates that 6(9) = 6(4) + 6(5) is below.

$6\times 9 = 6\times 4 +6\times 5$

Step-by-step explanation:

Consider a Rectangle ABCD segregate in two Rectangle by a Dash Line

i.e Rectangle AEFD  and

    Rectangle EBCF

We Know

$\textrm{Area of Rectangle}=Length\times Width$

For Rectangle ABCD we have

Length = 6

Width = 9

$\therefore \textrm{Area of Rectangle ABCD}=6\times 9$..........( 1 )

So For Rectangle AEFD we have

Length = 6

Width = 4

$\therefore \textrm{Area of Rectangle AEFD}=6\times 4$..........( 2 )

Similarly, For Rectangle EBCF we have

Length = 6

Width = 5

$\therefore \textrm{Area of Rectangle EBCF}=6\times 5$..........( 3 )

Now,

$\textrm{Area of Rectangle ABCD}=\textrm{Area of Rectangle AEFD}+\textrm{Area of Rectangle EBCF}$

Substituting the values we get

$6\times 9 = 6\times 4 +6\times 5$

Which is equal to

So, 6(9) = 6(4) + 6(5).