Question

Tom is making a rectangular garden with a length of x + 45 and a width of x + 75.

Write and solve an equation that can be used to find the value of x if the perimeter is 300 feet

Question 8 options:

2(x+45) + 2(x + 75) = 300

x = 60


2(x+45) + 2(x + 75) = 300

x = 15


(x+45) + (x+ 75) = 300

x = 120

Answer 1

To find the value of \( x \) for the given rectangular garden with a perimeter of 300 feet, we start with the formula for the perimeter of a rectangle, which is:

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

In this case, the length is \( x + 45 \) and the width is \( x + 75 \). The equation for the perimeter is:

\[
P = 2 \times ((x + 45) + (x + 75))
\]

Setting the perimeter equal to 300 feet, we can write the equation as:

\[
2 \times ((x + 45) + (x + 75)) = 300
\]

Now, simplify the equation:

\[
2 \times (2x + 120) = 300
\]

Expanding the left side gives:

\[
4x + 240 = 300
\]

Next, we solve for \( x \) by isolating it:

1. Subtract 240 from both sides:

\[
4x = 300 - 240
\]

\[
4x = 60
\]

2. Divide by 4:

\[
x = 15
\]

So, the correct equation is:

\[
2(x + 45) + 2(x + 75) = 300
\]

And the corresponding solution is:

\[
x = 15
\]

Thus, the correct option is:

**2(x + 45) + 2(x + 75) = 300
x = 15**