the areas of two rectangles are 15 square inches and 16 square inches. the length and width of both figures are whole numbers. if the rectangles have the same width, what is the greatest possible value for their widths? please show work
please
area of first = length1 x width
15 = length1 x width
width = 15/length1
area of 2nd:
16 = length2 x width
width = 16/length2
so length2/length1 = 16/15
the length of the first is 15, its width is 1
the length of the 2nd is 16, its width is 1
the largest value of the width has to be 1
To find the greatest possible value for the widths of the rectangles, we need to consider the factors of the areas of both rectangles.
The factors of 15 are: 1, 3, 5, and 15.
The factors of 16 are: 1, 2, 4, 8, and 16.
Since the rectangles have the same width, the width must be the same factor for both areas.
Since the greatest common factor of 15 and 16 is 1, the greatest possible value for their widths is 1.
To find the greatest possible width of the rectangles, we need to identify the common factors of the two given areas (15 and 16) and find the greatest whole number among them.
The factors of 15 are 1, 3, 5, and 15.
The factors of 16 are 1, 2, 4, 8, and 16.
Since the rectangles have the same width, the greatest common factor (GCF) of the two areas represents the possible width of the rectangles.
The common factors of 15 and 16 are 1. Therefore, the greatest possible width for the rectangles is 1 inch.
Now, let's verify this by calculating the length of each rectangle using the given areas and the width (1 inch):
For the first rectangle:
Area = length * width
15 square inches = length * 1 inch
length = 15 inches
For the second rectangle:
Area = length * width
16 square inches = length * 1 inch
length = 16 inches
So, the rectangles with a common width of 1 inch would have lengths of 15 inches and 16 inches, respectively.