Question

The table shows the area of two rugs a preschool teacher has in her room. She places the two rugs together to make one big rug.Blue=8(X+1/2Red=10(X+2/5What is the area in square units of the new rug, in factored form?

Answer 1

The area of the new rug in factored form is 2(9x + 4) square units.

How to find the area of the new rug

To find the area of the new rug, add the areas of the two smaller rugs.

Adding the Areas:

Area of blue rug: 8(x + 1/2)

Area of red rug: 10(x + 2/5)

Total Area = 8(x + 1/2) + 10(x + 2/5)

Combining like terms:

Distribute the constants:

Total Area = 8x + 4 + 10x + 4

Combine x terms:

Total Area = (8x + 10x) + (4 + 4)

Simplify:

Total Area = 18x + 8

Factored form:

The expression 18x + 8 can be factored as 2(9x + 4).

Therefore, the area of the new rug in factored form is 2(9x + 4) square units.

Answer 2

The area of blue rug is 8(x + 1/2).

The area of red rug is 10(x + 2/5).

The total area will be :

`\begin{gathered} 8(x+(1)/(2))+10(x+(2)/(5))=(8x+4)+(10x+4) \\ =8x+4+10x+4 \\ =18x+8 \end{gathered}`

Factor out 18 :

`\begin{gathered} 18x+8\Rightarrow18(x+(8)/(18)) \\ \Rightarrow18(x+(4)/(9)) \end{gathered}`

The answer is 18(x + 4/9)