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A rectangular bedroom is 2 ft longer than it is wide. Its area is 99 ft^2. What is the width of the room?

Respuesta :

Let

  • B=x
  • L=x+2

ATQ

[tex]\\ \sf\longmapsto LB=Area[/tex]

[tex]\\ \sf\longmapsto x(x+2)=99[/tex]

[tex]\\ \sf\longmapsto x^2+2x=99[/tex]

[tex]\\ \sf\longmapsto x^2+2x-99=0[/tex]

[tex]\\ \sf\longmapsto x^2+11x-9x-99=0[/tex]

[tex]\\ \sf\longmapsto x(x+11)-9(x+11)[/tex]

[tex]\\ \sf\longmapsto (x-9)(x+11)=0[/tex]

Take positive

[tex]\\ \sf\longmapsto x=9[/tex]

Hi1315

Answer:

[tex]length = 11ft \\ width = 9ft[/tex]

Step-by-step explanation:

Let the wide be x

length = x+2

Area = Length * width

[tex]99 = x(x + 2) \\ [/tex]

Now let's solve the expression and find the width

[tex]x(x + 2) = 99 \\ {x}^{2} + 2x = 99 \\ {x}^{2} + 2x - 99 = 0 \\ {x}^{2} + 2x = 99 \\ {x}^{2} + 2x + 1 = 99 + 1 \\ {(x + 1)}^{2} = 100 \\ x + 1 = \sqrt{100} \\ x + 1 = ±10 \\ x = ±10 - 1 \\ \\ x = + 10 - 1 \\ = 9 \\ \\ x = - 10 - 1 \\ = - 11[/tex]

As a negative number cannot be get as a length

We have to get the positive number as the length

so,

[tex]x = 9ft[/tex]

[tex]x + 2 = 9 + 2 \\ = 11ft[/tex]

hope this helps you.

let me know if you have another questions :-)

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