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

Step-by-step 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