Question

John was told that the rectangle had a side length of
5
x
+
20

f
t
5x+20 ft and the other side length was
2
x
+
23.
2x+23. If the perimeter of the rectangle was
208.5

f
t
208.5 ft then what is the value of
x
x

Answer 1

John found that the perimeter of a square is
4
x
+
21
4x+21
f
t
ft . If the perimeter's length is
100

f
t
100 ft what is the value of
x
x ?

Answer 2

To find the value of \( x \) in the rectangle's side lengths, we first need to use the formula for the perimeter of a rectangle. The perimeter \( P \) of a rectangle is given by:

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

Given the side lengths:

- Length \( = 5x + 20 \) ft
- Width \( = 2x + 23 \) ft

We can plug these into the perimeter formula:

\[
208.5 = 2 \times ((5x + 20) + (2x + 23))
\]

Simplifying inside the parentheses:

\[
208.5 = 2 \times (5x + 20 + 2x + 23)
\]
\[
208.5 = 2 \times (7x + 43)
\]

Next, we'll distribute the 2:

\[
208.5 = 14x + 86
\]

Now, we solve for \( x \) by isolating \( x \). First, subtract 86 from both sides:

\[
208.5 - 86 = 14x
\]
\[
122.5 = 14x
\]

Next, divide by 14:

\[
x = \frac{122.5}{14}
\]
\[
x = 8.75
\]

Thus, the value of \( x \) is \( \boxed{8.75} \).

Answer 3

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

\[
P = 4 \times \text{side length}
\]

In this case, we know that the perimeter is represented as \( 4x + 21 \) ft, and it's given that \( P = 100 \) ft. Therefore, we can set up the equation:

\[
4x + 21 = 100
\]

Now, we'll solve for \( x \).

First, subtract 21 from both sides:

\[
4x + 21 - 21 = 100 - 21
\]
\[
4x = 79
\]

Next, divide both sides by 4:

\[
x = \frac{79}{4}
\]
\[
x = 19.75
\]

Thus, the value of \( x \) is \( \boxed{19.75} \).