Question

But it decides to build a square room for his movies and music collection if the area of the room is 16 X squared -24X +9 ft.² what is the length of the one side of the room

Answer 1

The length of the one side of the square room(a) = (4x - 3) ft

Explanation:

Given,

The area of the room = 16
`X^2` - 24X + 9
`ft^2`

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)`

Where, a is the side of the square

∴
`a^(2)` = 16
`X^2` - 24X + 9

⇒
`a^(2)` =
`(4X)^2` - 2(4X)(3) +
`3^(2)`

Using the algebraic identity,

`(a-b)^(2) =a^(2) -2ab+b^(2)`

⇒
`a^(2)` =
`(4x-3)^2`

⇒ a = (4x - 3) ft

∴ The length of the one side of the square room(a) = (4x - 3) ft