On the same base and with the same altitude, consider a parallelogram (area P), a triangle (area R), and a rectangle (area A).\nWhich relation is always true?

Difficulty: Easy

Correct Answer: P=2R

Explanation:


Introduction / Context:
For plane figures sharing the same base length b and altitude h, their areas follow standard formulas: parallelogram P = b*h, rectangle A = b*h, triangle R = (1/2)*b*h. Comparing these immediately yields the fixed relations among P, A, and R.


Given Data / Assumptions:

  • All figures share base b and altitude h.


Concept / Approach:
Write each area in terms of b and h and compare.


Step-by-Step Solution:

Parallelogram: P = b * hRectangle: A = b * hTriangle: R = (1/2) * b * hTherefore P = A and P = 2R, so in particular P = 2R.


Why Other Options Are Wrong:

  • P=R: False; triangle area is half.
  • P=A/2: False; parallelogram equals rectangle, not half.


Final Answer:
P=2R

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