Verified Answer :

To find this you know that the A of a square = s^2

So the length of one side equals \(s = \sqrt{16 x^{2} +72x+81}\)

Since this is a perfect square, it would equal \(A = (4x+9)^{2}\)

And \(s = \sqrt{(4x+9)^{2}} = 4x+9\)

Also you know it is a perfect square because the first and last terms are perfect squares :) :D

abidemiokin

The length of one side of the room is 4x + 9 units

The formula for calculating the area of a square is expressed as:

A = L² where:

L is the side length of the square

Given the expression representing the area of the square room as:

\(A = 16x^2+72x+81\)

Factorize the expression:

\(A = 16x^2+72x+81\\A = 16x^2+36x+36x+81\\A = 4x(4x+9)+9(4x+9)\\A = (4x+9)(4x+9)\\A=(4x+9)^2\)

Comparing this with the formula:

\(L^2= (4x+9)^2\\L = 4x+9\)

Hene the length of one side of the room is 4x + 9 units.

Learn more here: https://brainly.com/question/17182640

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