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.
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