Question

John found that the perimeter of a square is 4 𝑥 + 20 4x+20 𝑓 𝑡 ft . If the perimeter's length is 96 𝑓 𝑡 96 ft what is the value of 𝑥 x ?

Answer 1

To find the value of \( x \), we start by using the formula for the perimeter of a square, which is given by:

\[
P = 4s
\]

where \( s \) is the length of one side of the square.

According to the problem, the perimeter can also be expressed as \( 4x + 20 \) ft. We set this equal to the given perimeter of 96 ft:

\[
4x + 20 = 96
\]

Now, we need to solve for \( x \). First, we can isolate \( 4x \) by subtracting 20 from both sides:

\[
4x = 96 - 20
\]

This simplifies to:

\[
4x = 76
\]

Next, we divide both sides by 4 to solve for \( x \):

\[
x = \frac{76}{4}
\]

Calculating this gives:

\[
x = 19
\]

Thus, the value of \( x \) is:

\[
\boxed{19}
\]