36unit squares are joined to form a rectangle with lest perimeter what is the perimeter of rectangle?
26 units
To find the perimeter of the rectangle formed by joining 36 unit squares, we need to determine the dimensions of the rectangle.
Let's consider that the rectangle is formed by joining m unit squares horizontally and n unit squares vertically.
From the given information, we know that the total number of unit squares is 36. Therefore, we can represent this as an equation:
m * n = 36
The next step is to find the dimensions of the rectangle (m and n) that will minimize the perimeter.
To minimize the perimeter, we need to find the pair of positive integers (m and n) that satisfies the equation m * n = 36 while minimizing the sum of the sides.
We know that the perimeter of a rectangle is calculated by the formula:
Perimeter = 2 * (length + width)
In this case, the length is represented by m units and the width by n units. The sum of sides is therefore:
Sum of sides = m + n
To minimize the sum of sides (m + n), we need to find the pair of positive integers (m and n) whose product is 36 and the sum is the lowest possible value.
The pairs of positive integers that satisfy the equation m * n = 36 are:
m=1, n=36
m=2, n=18
m=3, n=12
m=4, n=9
m=6, n=6
Among these pairs, the pair (m=6, n=6) will yield the lowest sum of sides, which is 6 + 6 = 12.
Therefore, the dimensions of the rectangle should be 6 units by 6 units.
Using the formula for perimeter, we can now calculate the perimeter of the rectangle:
Perimeter = 2 * (length + width)
Perimeter = 2 * (6 + 6)
Perimeter = 2 * 12
Perimeter = 24
So, the perimeter of the rectangle formed by joining 36 unit squares is 24 units.