Question

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?

Answer 1

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 \( 7.5 \).