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?

Answer 1

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.