Respuesta :
Answer:
The dimensions of the room are length is 16 feet and the width is 11 feet.
Step-by-step explanation:
Given:
The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide.
Now, to get the dimensions.
Let the width be [tex]x.[/tex]
So, the length = [tex]x+5.[/tex]
Area = 176 square foot.
So, we put formula of area to get the dimensions:
Area = length × width.
[tex]176=(x+5)\times x[/tex]
[tex]176=x^2+5x[/tex]
Subtracting boths sides by 176 we get:
[tex]0=x^2+5x-176\\x^2+5x-176=0[/tex]
On solving the equation:
[tex]x^2+16x-11x-176=0\\x(x+16)-11(x+16)=0\\(x+16)(x-11)=0[/tex]
As,
[tex]x+16[/tex] = 0
[tex]x=-16[/tex]
So, we would not take the negative result.
Thus,
[tex]x-11=0\\x=11[/tex]
So, the width = 11 feet.
Now, to get the length by substituting the value of [tex]x[/tex]:
[tex]x+5\\=11+5\\=16[/tex]
The length = 16 feet.
Therefore, the dimensions of the room are length is 16 feet and the width is 11 feet.
