Question

John found that the perimeter of a square is 2x+302x+30 ft . If the perimeter's length is 128 ft 128 ft what is the value of x ?

Answer 1

The perimeter \( P \) of a square is given by the formula:

\[
P = 4s
\]

where \( s \) is the length of one side of the square. Since the problem states that the perimeter can also be represented as \( 2x + 302x + 30 \) ft, we can first simplify that expression.

Combine the terms:

\[
2x + 302x + 30 = 304x + 30
\]

Now we know the perimeter is also given as:

\[
304x + 30 = 128
\]

Next, we can solve for \( x \). Start by isolating the term with \( x \):

\[
304x + 30 = 128
\]

Subtract 30 from both sides:

\[
304x = 128 - 30
\]
\[
304x = 98
\]

Now, divide both sides by 304:

\[
x = \frac{98}{304}
\]

This fraction can be simplified:

\[
x = \frac{98 \div 2}{304 \div 2} = \frac{49}{152}
\]

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

\[
\boxed{\frac{49}{152}}
\]