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 ?

Question

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:

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