A triangle and a parallelogram are constructed on the same base and have equal areas. If the altitude of the parallelogram is 100 m, find the altitude of the triangle.

Introduction / Context:When a triangle and a parallelogram share the same base, comparing their areas reduces to comparing altitudes. This classic relation helps convert one altitude to the other directly.

Given Data / Assumptions:

• Same base length b for both shapes.
• Parallelogram altitude h_p = 100 m.
• Areas are equal.

Concept / Approach:Area of triangle: A_t = (1/2) * b * h_t. Area of parallelogram: A_p = b * h_p. With A_t = A_p and same base b, the altitudes relate by (1/2) * b * h_t = b * h_p, hence h_t = 2 * h_p.

Step-by-Step Solution:

Verification / Alternative check:Pick b = 10 m. Then A_p = 10 * 100 = 1,000 m^2. For triangle to have 1,000 m^2: (1/2) * 10 * h_t = 1,000 ⇒ h_t = 200 m. Confirms result.

Why Other Options Are Wrong:

• 300m, 400m: Would make the triangle area larger than the parallelogram.
• 100m: Would make the triangle area half of the parallelogram area, not equal.

Common Pitfalls:

• Forgetting that the triangle area has the 1/2 factor while the parallelogram does not.
• Assuming altitudes are equal when areas are equal.

Final Answer:200m