Question

the area of a square room is 16x^2+72x+81. what is the length of one side of the room

Answer 1

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

Answer 2

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