A triangle and a parallelogram are constructed on the same base, and their areas are equal. If the altitude (height) of the parallelogram is 100 m, what is the altitude (height) of the triangle?

Introduction / Context:
This question tests area formulas for a triangle and a parallelogram when both share the same base. The area of a parallelogram is base * height, while the area of a triangle is (1/2) * base * height. If they are built on the same base and have equal areas, the only way to compensate for the factor 1/2 in the triangle formula is for the triangle's altitude to be twice the parallelogram's altitude. This is a direct relationship question and does not require any actual base value.

Given Data / Assumptions:

• Triangle and parallelogram have the same base
• Areas are equal
• Parallelogram altitude = 100 m
• Area(parallelogram) = base * height
• Area(triangle) = (1/2) * base * height

Concept / Approach:
Set areas equal: base*Hp = (1/2)*base*Ht. Cancel base and solve for Ht in terms of Hp.

Step-by-Step Solution:
base*Hp = (1/2)*base*Ht Cancel base (same and non-zero): Hp = (1/2)*Ht Ht = 2*Hp Ht = 2*100 = 200 m

Verification / Alternative check:
If base is any value b, parallelogram area = b*100. Triangle with height 200 has area = (1/2)*b*200 = b*100, exactly equal. This confirms the relationship is correct for any base.

Why Other Options Are Wrong:
100 m would make the triangle area half of the parallelogram area. 300 m and 400 m make triangle area larger than the parallelogram. 150 m does not offset the 1/2 factor correctly.

Common Pitfalls:
Forgetting the 1/2 in triangle area, assuming triangle and parallelogram heights must be equal, or mixing up base and height roles.

Final Answer:
The altitude of the triangle is 200 m.