Question

John was told that the rectangle had a side length of 2x +12 ft 2x+12 ft and the other side length was 5x+22. If the perimeter of the rectangle was 110 ft then what is the value of x ?
x=_____ft

Answer 1

To find the value of \( x \), we'll start by using the formula for the perimeter of a rectangle, which is given by:

\[
P = 2(l + w)
\]

where \( l \) is the length and \( w \) is the width. In this case, we have:

- Length \( l = 2x + 12 \) ft
- Width \( w = 5x + 22 \) ft

According to the problem, the perimeter \( P \) is 110 ft. Therefore, we can set up the equation:

\[
2((2x + 12) + (5x + 22)) = 110
\]

Let's simplify the equation step by step:

1. Combine the expressions inside the parentheses:

\[
2(2x + 12 + 5x + 22) = 110
\]
\[
2(7x + 34) = 110
\]

2. Divide both sides by 2:

\[
7x + 34 = 55
\]

3. Subtract 34 from both sides:

\[
7x = 55 - 34
\]
\[
7x = 21
\]

4. Now, divide by 7:

\[
x = \frac{21}{7} = 3
\]

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

\[
\boxed{3} \text{ ft}
\]