The length of the one side of the square room(a) = (4x - 3) ft
Step-by-step explanation:
Given,
The area of the room = 16[tex]X^2[/tex] - 24X + 9 [tex]ft^2[/tex]
Let 'a' be the length of the one side of the room.
To find, the length of the one side of the room(a) = ?
We know that,
The area of the square = [tex]a^{2}[/tex]
Where, a is the side of the square
∴ [tex]a^{2}[/tex] = 16[tex]X^2[/tex] - 24X + 9
⇒ [tex]a^{2}[/tex] = [tex](4X)^2[/tex] - 2(4X)(3) + [tex]3^{2}[/tex]
Using the algebraic identity,
[tex](a-b)^{2} =a^{2} -2ab+b^{2}[/tex]
⇒ [tex]a^{2}[/tex] = [tex](4x-3)^2[/tex]
⇒ a = (4x - 3) ft
∴ The length of the one side of the square room(a) = (4x - 3) ft
