Evaluating geometric division possibilities for a rectangle
Question
Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:
Which of the above statements is/are correct?
Options
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Explanation
Evaluate the geometric partitions of the 20 × 8 rectangle:
Statement 1: Can we cut it exactly into 4 squares? The text does not say the squares must be identical. Cut an 8 × 8 square from the edge. Remaining area = 12 × 8. Cut another 8 × 8 square. Remaining area = 4 × 8. Cut the 4 × 8 rectangle in half to yield two 4 × 4 squares. We have exactly 4 squares (two 8 × 8, two 4 × 4) that perfectly consume the sheet without waste. Valid.
Statement 2: Can we cut it into 10 equal-area triangles? Divide the rectangle into 5 equal vertical strips of 4 × 8. Draw a single diagonal line across each of these 5 strips. This splits every rectangle into 2 identical right-angled triangles. Total = 5 × 2 = 10 equal-area triangles. Valid.
Answer: (c).
Question details
Year
2022
Paper
CSAT
Question
Q59
Section
Numerical Ability
Sub-topic
Geometry / Mensuration
Type
Statement-based
Difficulty
Medium
Source hint
Rectangular sheet 20cm by 8cm
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