John was told that the rectangle had a side length of

Question

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:

\[ \boxed{7.5} \]