Final answer:
The volume of a right triangular prism with its height equal to the triangular base's leg length is 1/2 x³ cubic units. The provided answer choices do not include this expression, suggesting an error in the options.
Step-by-step explanation:
The question asks for the expression that represents the volume of a right triangular prism, where the height of the prism is equal to the leg length of the triangular base. To find the volume of the prism (V), we use the formula V = base area × height. The base of the prism is a right triangle, so the area of the base triangle (A) is given by A = 1/2 × base × height. Since the base and height of the triangle are both x units (as indicated by the term 'leg length'), the area becomes A = 1/2 × x × x = 1/2 x². Therefore, the volume of the prism can be calculated as V = A × height = (1/2 x²) × x = 1/2 x³. Since none of the options a), b), c) or d) correctly represents this volume, it seems there might have been an error in the options provided.