A square patio rug has side lengths of 1/3(x+2) inches
a. Write a linear expression involving the perimeter of the square, P in terms of x.
b. Solve for x in terms of P.
a square has FOUR equal sides
4 * 1/3(x+2) = 4/3 x + 8/3 = P
4/3 x = P - 8/3
4 x = 3 P - 8
x = 3/4 P - 2
To write a linear expression involving the perimeter of the square, let's start by finding the equation for the perimeter of the square.
The perimeter of a square is calculated by summing the lengths of all four sides. Since all sides of a square are equal, we can express the perimeter as P = 4s, where s represents the length of one side.
Given that the length of one side of the square patio rug is 1/3(x + 2) inches, we can substitute this expression into the perimeter equation:
P = 4s = 4(1/3(x + 2)) = 4/3(x + 2)
So, the linear expression involving the perimeter of the square, P, in terms of x is P = 4/3(x + 2).
To solve for x in terms of P, we need to isolate x in the equation P = 4/3(x + 2).
Let's start by distributing the 4/3 to the terms inside the parentheses:
P = 4/3(x + 2) = 4/3 * x + 4/3 * 2 = 4/3x + 8/3
Next, let's subtract 8/3 from both sides of the equation to isolate the x term:
P - 8/3 = 4/3x + 8/3 - 8/3
P - 8/3 = 4/3x
To get x alone, we need to multiply both sides by 3/4:
3/4 * (P - 8/3) = 3/4 * (4/3x)
(3/4)P - (3/4)(8/3) = x
Simplifying the expression, we get:
(3/4)P - 2 = x
So, x in terms of P is x = (3/4)P - 2.