Final answer:
To find the value of x in the rectangle with a perimeter of 70 feet, we use the perimeter formula. By setting up the correct equation and solving for x, we find that x equals 13 feet.
Step-by-step explanation:
The perimeter of a rectangle is the total length of its four sides. If you know the length (LL) and the width (WW) of a rectangle, you can use the formula for perimeter (PP):
P=2L+2WP=2L+2W
Alternatively, the formula can be expressed as:
P=2×(L+W)P=2×(L+W)
These formulas are derived by adding up the lengths of all four sides of the rectangle, where each side contributes either the length or the width. The multiplication by 2 accounts for the fact that there are two sides of each length and two sides of each width.
So, if you have the length and width of a rectangle, plug these values into the formula to find its perimeter.
To find the value of x for the rectangle given the perimeter is 70 feet, and the sides are represented as x + 4 and 2x - 8, we need to use the perimeter formula for a rectangle, which is P = 2(l + w). Here, let the length be x + 4 and the width be 2x - 8.
The perimeter equation set up is:
2(x + 4) + 2(2x - 8) = 70
Simplifying, we get:
2x + 8 + 4x - 16 = 70
Combining like terms:
6x - 8 = 70
Adding 8 to both sides:
6x = 78
Dividing by 6:
x = 13
Therefore, the value of x is 13 feet.