Question

John was told that the rectangle had a side length of
5
x
+
17

f
t
5x+17 ft and the other side length was
3
x
+
21.
3x+21. If the perimeter of the rectangle was
196.0

f
t
196.0 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 of a rectangle, which is given by:

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

In this case, the length is \( 5x + 17 \) and the width is \( 3x + 21 \). Therefore, we can express the perimeter as:

\[
196 = 2((5x + 17) + (3x + 21))
\]

First, simplify the expression inside the parentheses:

\[
(5x + 17) + (3x + 21) = 5x + 3x + 17 + 21 = 8x + 38
\]

Then, insert this back into the perimeter formula:

\[
196 = 2(8x + 38)
\]

Now, divide both sides by 2 to simplify:

\[
98 = 8x + 38
\]

Next, subtract 38 from both sides:

\[
98 - 38 = 8x
\]
\[
60 = 8x
\]

Now, divide both sides by 8 to solve for \( x \):

\[
x = \frac{60}{8} = 7.5
\]

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

\[
\boxed{7.5}
\]