A square of side a has the same area as a triangle with base a. What is the altitude (height) of the triangle?

Introduction / Context:This is a direct comparison of area formulas between a square and a triangle built on the same base length a. Translate equality of areas into equality of formulas and solve for height.

Given Data / Assumptions:

• Square area = a^2.
• Triangle area = (1/2) * base * height = (1/2) * a * h.

Concept / Approach:Set a^2 = (1/2) * a * h and solve for h.

Step-by-Step Solution:

Final Answer:2a