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Q59·CSAT · Prelims 2022

Evaluating geometric division possibilities for a rectangle

NumericalGeometry / MensurationStatement-basedMedium

Question

Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:

1It is possible to cut the sheet exactly into 4 square sheets.
2It is possible to cut the sheet into 10 triangular sheets of equal area.

Which of the above statements is/are correct?

Options

a

1 only

b

2 only

c

Both 1 and 2

Answer
d

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.

In geometric packing problems, carefully check modifiers; if a constraint like "identical" or "equal size" is missing (as in Statement 1), variable-sized combinations are perfectly legal.

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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