12 equal square are placed to feet in a rectangle of diagonal 5 cm there are three rows containing four square each no gaps are left between adjacent square what is the area of each square?
Answers
Answer:
Area of each square is 1 cm^2.
Step-by-step explanation:
Given details:
Rectangle has diagonal of 5 cm.
12 equal squares are fit into the rectangle in 3 rows with 4 squares in each row.
Solution:
Let the side the square be 'x'.
Therefore,
Length of the rectangle will be x + x + x + x = 4x
Breadth of the rectangle will be x + x + x = 3x
According to Pythagoras theorem,
5^2 = (4x)^2 + (3x)^2
25 = 16x^2 + 9x^2
25 = 25x^2
x = 1
Side of the square (x) = 1 cm.
Therefore,
Area of the square = side * side = 1 * 1 = 1 cm^2
Answer:
3 Possibilities
0.1724 cm²
0.625 cm²
1 cm²
Step-by-step explanation:
12 equal square are placed to feet in a rectangle of diagonal 5 cm there are three rows containing four square each no gaps are left between adjacent square what is the area of each square?
Let say side of square = s cm
Squares are placed into a * b
Then sides of rectangle are as & bs cm
where a & b are integers and placement of squares in rectangles
Area of each square = s² cm²
Area of 12 squares = 12s² cm²
Area of rectangle = as * bs = abs² cm²
=> abs² = 12s²
=> ab = 12
Possible integers values for ab
(1 , 12) , (2 , 6) , ( 3 ,4)
(Diagonal of rectangle)² = (as)² + (bs)²
=> 5² = s²(a² + b²)
=> s² = 25/(a² + b²)
ab = (1 , 12)
s² = 25/(1² + 12²) = 25/145 = 0.1724 cm² ( Placed into 1 * 12)
ab = (2 , 6)
s² = 25/(2² + 6²) = 25/40 = 0.625 cm² ( Placed into 2 * 6)
ab = (3 , 4)
s² = 25/(3² + 4²) = 25/25 = 1 cm² ( Placed into 3 * 4)
3 Possible squares
0.1724 cm²
0.625 cm²
1 cm²