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
- 24X + 9 ![ft^2](https://tex.z-dn.net/?f=ft%5E2)
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 = ![a^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D)
Where, a is the side of the square
∴
= 16
- 24X + 9
⇒
=
- 2(4X)(3) + ![3^{2}](https://tex.z-dn.net/?f=3%5E%7B2%7D)
Using the algebraic identity,
![(a-b)^{2} =a^{2} -2ab+b^{2}](https://tex.z-dn.net/?f=%28a-b%29%5E%7B2%7D%20%3Da%5E%7B2%7D%20-2ab%2Bb%5E%7B2%7D)
⇒
= ![(4x-3)^2](https://tex.z-dn.net/?f=%284x-3%29%5E2)
⇒ a = (4x - 3) ft
∴ The length of the one side of the square room(a) = (4x - 3) ft