The perimeter of the rectangle below is 42 units. Find the value of y.
Rectangle side 1: 3y-3
Side 2: 2y-1
To find the value of y, we need to use the formula for the perimeter of a rectangle, which is given by P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
Given that the perimeter of the rectangle is 42 units, we can set up the equation as follows:
42 = 2(3y-3 + 2y-1)
Let's simplify this equation step-by-step.
First, we can distribute the 2 to the terms inside the parentheses:
42 = 2(3y-3) + 2(2y-1)
42 = 6y - 6 + 4y - 2
Next, we can combine like terms on the right side of the equation:
42 = 10y - 8
Now, let's isolate the variable y. We can start by adding 8 to both sides of the equation:
42 + 8 = 10y - 8 + 8
50 = 10y
Finally, we can solve for y by dividing both sides of the equation by 10:
50/10 = 10y/10
5 = y
Therefore, the value of y is 5.
To find the value of y, we need to use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (length + width)
Given that "Side 1" is represented by 3y-3 and "Side 2" is represented by 2y-1, we can substitute these values into the formula:
42 = 2 * ((3y-3) + (2y-1))
Now, let's simplify the equation:
42 = 2 * (3y + 2y - 3 - 1)
42 = 2 * (5y - 4)
42 = 10y - 8
To solve for y, we need to isolate it on one side of the equation. Let's do that:
42 + 8 = 10y
50 = 10y
To find the value of y, divide both sides of the equation by 10:
50/10 = y
5 = y
So, the value of y is 5.
2(3y-3 + 2y-1) = 42
5y-4 = 21
y=5