19. The area of a given rectangle is \( 150 \mathrm{~cm}^{2} \). If Side \( A \) is 10 cm and Side \( B \) is \( \sqrt{3 x} \), what is the value of \( x \) ? \( \begin{array}{llll}\text { A. } 75 \mathrm{~cm} & \text { B. } 15 \mathrm{~cm} & \text { C. } 225 \mathrm{~cm} & \text { D. } 3 \mathrm{~cm}\end{array} \) rt Answer

To find the value of \( x \) given the area of the rectangle and the expressions for sides \( A \) and \( B \), follow these steps: 1. **Given Information:** - Area of the rectangle, \( \text{Area} = 150 \, \text{cm}^2 \) - Side \( A = 10 \, \text{cm} \) - Side \( B = \sqrt{3x} \) 2. **Area Formula:** \[ \text{Area} = A \times B \] Substitute the given values: \[ 150 = 10 \times \sqrt{3x} \] 3. **Solve for \( \sqrt{3x} \):** \[ \sqrt{3x} = \frac{150}{10} = 15 \] 4. **Square Both Sides to Eliminate the Square Root:** \[ (\sqrt{3x})^2 = 15^2 \] \[ 3x = 225 \] 5. **Solve for \( x \):** \[ x = \frac{225}{3} = 75 \] **Final Answer:** **A. 75 cm**