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Twelve equal squares are placed to fit in at rectangle of diagonal 5 cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square?
  • a)
    5/7 sq cm
  • b)
    7/5 sq cm 5
  • c)
    1 sq cm
  • d)
    25/12 sq cm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Twelve equal squares are placed to fit in at rectangle of diagonal 5 c...
Given:
- A rectangle of diagonal 5 cm
- 12 equal squares arranged in 3 rows of 4 each
- No gaps between adjacent squares

To Find: Area of each square

Solution:
- Let's assume the side of each square be "x"
- Let the length and width of the rectangle be "l" and "w" respectively
- We know that the diagonal of a rectangle is given by the Pythagorean theorem as: diagonal^2 = length^2 + width^2
- Substituting the given values, we get: 5^2 = l^2 + w^2
- Simplifying, we get: l^2 + w^2 = 25

- Since there are 12 squares arranged in 3 rows of 4 each, we get:
- 3x = w (width of the rectangle is equal to 3 times the side of each square)
- 4x = l (length of the rectangle is equal to 4 times the side of each square)

- Substituting the above values in the equation l^2 + w^2 = 25, we get:
- (4x)^2 + (3x)^2 = 25
- Simplifying, we get: x^2 = 1
- Therefore, area of each square = side^2 = x^2 = 1 sq cm

Therefore, the correct answer is option C: 1 sq cm.
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Community Answer
Twelve equal squares are placed to fit in at rectangle of diagonal 5 c...
Diagonal is 5
Sides are 3, 4cm
Total area 3*4 = 12
Area of each square = 12/12 = 1 sq cm
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Twelve equal squares are placed to fit in at rectangle of diagonal 5 cm. There are three rows containing four squares each. No gaps are left between adjacent squares. What is the area of each square?a)5/7 sq cmb)7/5 sq cm 5c)1 sq cmd)25/12 sq cmCorrect answer is option 'C'. Can you explain this answer?
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