The perimeter of a rectangle is 42 centimeters. The length of the rectangle can be represented by `\left(x+4\right)`and its width can be represented by `\left(2x-7\right)`. What are the dimensions of this rectangle in centimeters?
The formula for the perimeter of a rectangle is given by \(P = 2l + 2w\) where \(l\) is the length and \(w\) is the width.
Using the given information, we have:
\(2(x+4) + 2(2x-7) = 42\)
Simplifying the equation:
\(2x + 8 + 4x - 14 = 42\)
\(6x - 6 = 42\)
\(6x = 48\)
\(x = 8\)
Substituting the value of \(x\) back into the expressions for the length and width, we have:
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.
To find the dimensions of the rectangle, we need to set up an equation using the given information.
Let's represent the length of the rectangle as (x + 4) and its width as (2x - 7).
The formula for the perimeter of a rectangle is given by:
Perimeter = 2(length + width)
Substituting the values in the formula, we get:
42 = 2[(x + 4) + (2x - 7)]
Now we simplify the equation:
42 = 2[x + 4 + 2x - 7]
42 = 2[3x - 3]
42 = 6x - 6
Now, solve for x:
42 + 6 = 6x
48 = 6x
Divide both sides by 6 to isolate x:
48/6 = x
8 = x
Now, substitute this value of x back into our expressions for length and width:
Length = x + 4 = 8 + 4 = 12 cm
Width = 2x - 7 = 2(8) - 7 = 9 cm
Therefore, the dimensions of the rectangle are 12 cm by 9 cm.
To find the dimensions of the rectangle, we need to solve for the values of x first. Then we can substitute the value of x into the expressions for length and width to find the actual dimensions.
Let's start by finding the value of x.
The perimeter of a rectangle is given by the formula: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Given that P = 42 cm, we can substitute the expressions for length and width to get the equation:
42 = 2(x + 4) + 2(2x - 7)
Now we can simplify and solve the equation:
42 = 2x + 8 + 4x - 14
42 = 6x - 6
Adding 6 to both sides:
42 + 6 = 6x
48 = 6x
Dividing both sides by 6:
48/6 = x
8 = x
Now we have the value of x = 8.
To find the dimensions of the rectangle, we substitute the value of x into the expressions for length and width:
Length = x + 4 = 8 + 4 = 12 cm
Width = 2x - 7 = 2(8) - 7 = 16 - 7 = 9 cm
Therefore, the dimensions of the rectangle are 12 cm (length) and 9 cm (width).