Right-triangle length: Determine the hypotenuse of a right triangle whose perpendicular sides measure 12 units and 18 units.

Introduction / Context:
The Pythagorean theorem is widely used across electrical engineering and physics, particularly in phasor magnitude calculations (e.g., combining orthogonal voltage or current components). Here, it is applied directly to a geometric right triangle to find the hypotenuse from two perpendicular legs.

Given Data / Assumptions:

• Leg a = 12 units.
• Leg b = 18 units.
• Right triangle; hypotenuse c is opposite the right angle.

Concept / Approach:
Use the Pythagorean relation c^2 = a^2 + b^2. Then compute c = √(a^2 + b^2). This is the same vector magnitude formula used in phasor addition and impedance magnitude calculations in AC circuits.

Step-by-Step Solution:

Verification / Alternative check:
Express √468 = √(4 * 117) = 2√117. With √117 ≈ 10.8167, c ≈ 2 * 10.8167 ≈ 21.633, which matches the decimal computation and ensures consistent rounding.

Why Other Options Are Wrong:

• 4.24, 3.46, 2.16: These are much smaller than either leg and cannot be a hypotenuse (which must be the longest side).

Common Pitfalls:

• Accidentally subtracting the squares (appropriate only for projecting one component from hypotenuse and other leg).
• Rounding too early and producing a noticeably inaccurate result.

Final Answer:
21.63