Question

John was told that the rectangle had a side length of
5
𝑥
+
14

𝑓
𝑡
5x+14 ft and the other side length was
5
𝑥
+
26.
5x+26. If the perimeter of the rectangle was
230.0

𝑓
𝑡
230.0 ft then what is the value of
𝑥
x ?

Answer 1

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

\[
P = 2(\text{length} + \text{width})
\]

Given that one side length (width) is \( 5x + 14 \) ft and the other side length (length) is \( 5x + 26 \) ft, we can set up the equation for the perimeter:

\[
230 = 2((5x + 14) + (5x + 26))
\]

First, combine the expressions inside the parentheses:

\[
(5x + 14) + (5x + 26) = 5x + 14 + 5x + 26 = 10x + 40
\]

Now substitute this back into the perimeter equation:

\[
230 = 2(10x + 40)
\]

Next, simplify the equation by distributing the \( 2 \):

\[
230 = 20x + 80
\]

Now, to isolate \( x \), subtract \( 80 \) from both sides:

\[
230 - 80 = 20x \\
150 = 20x
\]

Now, divide both sides by \( 20 \):

\[
x = \frac{150}{20} \\
x = 7.5
\]

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

\[
\boxed{7.5}
\]