the perimeter if a rectangle is 42 centimeters. the lenght of a rectangle can be represented by (x+4), and its width acn be represented by (2x-7). what are the dimensions of this rectangle in centimeters?
P = 2L + 2W
42 = 2(x + 4) + 2(2x - 7)
42 = 2x + 8 + 4x - 14
48 = 6x
? = x
To find the dimensions of the rectangle, we need to set up an equation based on the given information.
Let's assume that the length of the rectangle is represented by (x + 4) centimeters, and the width is represented by (2x - 7) centimeters.
Perimeter of a rectangle is given by the formula:
Perimeter = 2(Length + Width)
In this case, the perimeter is given as 42 centimeters.
So we have:
42 = 2((x + 4) + (2x - 7))
Let's solve this equation step by step:
1. Distribute the 2 on the right side of the equation:
42 = 2x + 8 + 4x - 14
2. Combine like terms:
42 = 6x - 6
3. Add 6 to both sides of the equation:
42 + 6 = 6x - 6 + 6
48 = 6x
4. Divide both sides of the equation by 6:
48/6 = 6x/6
8 = x
Now we have the value of x. To find the dimensions of the rectangle, substitute the value of x back into the expressions for length and width:
Length = x + 4 = 8 + 4 = 12 centimeters
Width = 2x - 7 = 2(8) - 7 = 16 - 7 = 9 centimeters
Therefore, the dimensions of the rectangle are 12 centimeters by 9 centimeters.