A rectangle with perimeter 44cm is partitioned into 5 congruent rectangles .The perimeter of each of the congruent rectangle is ?
That depends on the size of the large rectangle. If the width is x and the height is y, and the dividing lines are vertical, then each small rectangle has perimeter 2(x/5 + 2y)
So, for example, some dimensions below yield results of
20x2: 2(4+2) = 12
15x7: 2(3+7) = 20
10x12: 2(2+12) = 28
5x17: 2(1+17) = 36
To find the perimeter of each congruent rectangle, we need to first determine the dimensions of the original rectangle.
Let's consider a rectangle with length L and width W.
The perimeter of a rectangle is given by: 2(L + W)
According to the given information, the perimeter of the original rectangle is 44 cm. So, we have:
2(L + W) = 44 cm
Now, we need to partition this rectangle into 5 congruent rectangles. Since the rectangles are congruent, they have the same dimensions.
Let's say the dimensions of each congruent rectangle are l and w.
If we partition the rectangle into 5 congruent rectangles, it means the length L is divided into 5 equal parts, and the width W remains the same.
So, the length l of each congruent rectangle is L/5, and the width w remains the same as W.
Now, let's calculate the perimeter of each congruent rectangle.
The perimeter of a rectangle is given by: 2(l + w)
Substituting the values, we have:
2(L/5 + W) = (2L/5) + 2W/5
Now, we can substitute the value of L from the original equation:
2L/5 + 2W/5 = 44/5
Simplifying the equation further, we have:
2L + 2W = 44
Divide the equation by 2, and we get:
L + W = 22
Now, we can substitute the value of L + W from this equation into the expression for the perimeter of each congruent rectangle:
(2L/5) + 2W/5 = (2(22)/5) = 44/5 = 8.8 cm
Therefore, the perimeter of each congruent rectangle is 8.8 cm.