Calculate the values of \( x, y \) and \( z \) in the cuboid shown below by following the steps given. If any of your answers are decimals, round them to 1 d.p. Step 1: Complete the equations below. \[ \begin{array}{l}\text { (a) } x^{2}+y^{2}=\ldots \\ \text { (b) } x^{2}+z^{2}=\ldots \\ \text { (c) } y^{2}+z^{2}=\ldots\end{array} \] Step 2: Use equations (b) and (c) to work out the value of \( x^{2}-y^{2} \).

To solve for \( x, y, \) and \( z \) in the cuboid, we first need to complete the equations given in Step 1. However, since the specific dimensions or values of the cuboid are not provided, I will assume that we are working with the relationships between the sides of a cuboid. Let's denote the lengths of the sides of the cuboid as follows: - Let \( a \) be the length, - Let \( b \) be the width, - Let \( c \) be the height. We can relate these dimensions to \( x, y, \) and \( z \) as follows: - Let \( x = a \), - Let \( y = b \), - Let \( z = c \). Now, we can complete the equations: 1. **Equation (a)**: \( x^2 + y^2 = a^2 + b^2 \) 2. **Equation (b)**: \( x^2 + z^2 = a^2 + c^2 \) 3. **Equation (c)**: \( y^2 + z^2 = b^2 + c^2 \) Next, we can express these equations in terms of \( x, y, z \): 1. \( x^2 + y^2 = a^2 + b^2 \) 2. \( x^2 + z^2 = a^2 + c^2 \) 3. \( y^2 + z^2 = b^2 + c^2 \) Now, we will use equations (b) and (c) to find \( x^2 - y^2 \). From equation (b): \[ x^2 + z^2 = a^2 + c^2 \quad \text{(1)} \] From equation (c): \[ y^2 + z^2 = b^2 + c^2 \quad \text{(2)} \] Now, we can subtract equation (2) from equation (1): \[ (x^2 + z^2) - (y^2 + z^2) = (a^2 + c^2) - (b^2 + c^2) \] This simplifies to: \[ x^2 - y^2 = a^2 - b^2 \] Thus, we have found the expression for \( x^2 - y^2 \): \[ x^2 - y^2 = a^2 - b^2 \] To find the specific values of \( x, y, \) and \( z \), we would need the actual dimensions \( a, b, \) and \( c \) of the cuboid. If you provide those values, I can help you calculate \( x, y, \) and \( z \) and round them to 1 decimal place as needed.