One side of a rectangle is four centimeters shorter than twice another side of the rectangle. Find the sides if we also know that the area of the rectangle is \( 16 \mathrm{~cm}^{2} \). shorter side: \( \square \mathrm{cm} \) longer side: \( \square \mathrm{cm} \)

Let’s denote the shorter side of the rectangle as \( x \) cm. According to the problem, the longer side can be expressed as \( 2x - 4 \) cm. The area of the rectangle is given by the formula: \[ \text{Area} = \text{length} \times \text{width} = x(2x - 4) \] Setting this equal to \( 16 \, \text{cm}^2 \): \[ x(2x - 4) = 16 \] Expanding the equation: \[ 2x^2 - 4x - 16 = 0 \] Dividing the entire equation by 2 simplifies it to: \[ x^2 - 2x - 8 = 0 \] Next, we can factor this quadratic equation: \[ (x - 4)(x + 2) = 0 \] The possible solutions for \( x \) are \( x = 4 \) or \( x = -2 \). Since a side length cannot be negative, we take \( x = 4 \) cm as the shorter side. Now we can find the longer side: \[ \text{Longer side} = 2(4) - 4 = 8 - 4 = 4 \, \text{cm} \] Thus, the sides of the rectangle are: shorter side: \( 4 \, \mathrm{cm} \) longer side: \( 4 \, \mathrm{cm} \) However, it appears both sides are equal, meaning the rectangle is actually a square!