John was told that the rectangle had side length of 5X +17 FT and the other side length was 3X + 21FT if the perimeter of the rectangle wise 196.0 FT then what is the value of vex?

1 answer

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

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

In this case, the length \( L \) is \( 5X + 17 \) feet and the width \( W \) is \( 3X + 21 \) feet.

We know the perimeter \( P \) is 196 feet, so we can set up the equation:

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

First, simplify the expression inside the parentheses:

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

Now substitute this back into the perimeter equation:

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

Next, divide both sides by 2:

\[ 8X + 38 = 98 \]

Now, subtract 38 from both sides:

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

Finally, divide both sides by 8:

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

Thus, the value of \( X \) is \( 7.5 \).