What is the area of a triangle with side lengths $30$, $40$, and $50$?

• A. $1200$
• B. $1000$
• C. $750$
• D. $600$

Answer: (D)

Verified step by step guidance

1. Identify the given side lengths of the triangle: 30, 40, and 50 units.
2. Recognize that these side lengths form a right triangle because 30² + 40² = 50² (i.e., 900 + 1600 = 2500).
3. Since it is a right triangle, use the formula for the area of a right triangle: \(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\).
4. Choose the two shorter sides as the base and height, so calculate the area as \(\frac{1}{2} \times 30 \times 40\).
5. Simplify the expression to find the area without calculating the final numeric value.