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pls help! will mark branliest!!! :)

The Smith family wants to build an addition to the back of their house as shown in the figure below. The area of the addition is (x²+10x-200) ft².


a) What is the length of the addition?

b) What is the area of the original house?

Pls Help Will Mark Branliest The Smith Family Wants To Build An Addition To The Back Of Their House As Shown In The Figure Below The Area Of The Addition Is X10 class=

Sagot :

MrRoyalidn

The area of the house is the amount of space on the house.

  • The length of the addition is x + 20
  • The area of the original house is [tex]x^2 + 30x + 200[/tex]

The length of the addition

The area of the addition is given as:

[tex]Area = x^2 + 10x - 200[/tex]

Expand

[tex]Area = x^2 + 20x - 10x - 200[/tex]

Factorize

[tex]Area = x(x + 20) - 10(x + 20)[/tex]

Factor out x + 20

[tex]Area = (x -10)(x + 20)[/tex]

The width of the addition is x - 10.

Hence, the length of the addition is x + 20

The area of the original house

The dimension of the original house is

x + 20 by x + 10

So, the area is:

[tex]Area =(x + 20)(x + 10)[/tex]

Expand

[tex]Area =x^2 + 20x + 10x + 200[/tex]

This gives

[tex]Area =x^2 + 30x + 200[/tex]

Hence, the area of the original house is [tex]x^2 + 30x + 200[/tex]

Read more about areas at:

https://brainly.com/question/24487155

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