Question

A square has a side length of 2x
inches. Find the values of x that will produce a square with an area that is less than or equal to 36 square inches.(1 point)
The value of x must be greater than 0 but less than or equal to
inches to produce a square with an area less than or equal to 36 square inches.

Answer 1

To find the values of \( x \) that will produce a square with an area less than or equal to 36 square inches, we start with the formula for the area of a square:

\[
\text{Area} = \text{side length}^2
\]

In this case, the side length of the square is \( 2x \) inches, so the area \( A \) is given by:

\[
A = (2x)^2 = 4x^2
\]

We want this area to be less than or equal to 36 square inches:

\[
4x^2 \leq 36
\]

Next, we divide both sides of the inequality by 4:

\[
x^2 \leq 9
\]

Now we take the square root of both sides. Since \( x \) must be greater than 0, we only consider the positive root:

\[
x \leq 3
\]

Thus, the values of \( x \) that will produce a square with an area less than or equal to 36 square inches are:

\[
0 < x \leq 3
\]

So, the value of \( x \) must be greater than 0 but less than or equal to 3 inches.