Mathematics: A square poster has an area measure of 324x^2 + 540x + 225 square units. Determine the side length of the poster.

A square poster has an area measure of 324x^2 + - id32425408994861, franciscovazquez623

Ответ:

josh3419

08.02.2022

$\huge\text{$(18x+15)$ units}$

Given the area, we need to find the side length. Let's start with the area equation for a square, where is the side length and is the area.

s^2=A

Substitute in the known value.

s^2=324x^2+540x+225

Now we need to factor the trinomial. The trinomial given for the area is a perfect square trinomial since 324 ( 18^2 ) and 225 ( 15^2 ) are both perfect squares.

We also know that a^2+2ab+b^2=(a+b)^2 , which we can use to factor.

$s^2=324x^2+540x+225\\s^2=(18x)^2+2(18x)(15)+15^2\\s^2=(18x+15)^2$

Now, take the square root of both sides to fully isolate .

$\sqrt{s^2}=\sqrt{(18x+15)^2}$

Keep in mind that the square root of any value squared is the original value.

$s=\boxed{18x+15}$

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A square poster has an area measure of 324x^2 + 540x + 225 square units. Determine the side length of the poster.

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