A piece of ribbon 25m long is cut into pieces of equal length.Is it possible to get a piece with irrational length?Explain.
no
"pieces of equal length" means that the ribbon's 25 m will be divided into a WHOLE NUMBER of pieces
the fraction representing the length of any piece will be 25 m, divided by an integer denominator ... a rational number
yes because of the number it use to make a integers on rational it is irrational. thank yoiu
To determine whether it is possible to get a piece with an irrational length, we need to consider the rationality of the resulting piece length after cutting the ribbon.
First, let's assume that the ribbon is cut into n equal pieces, where n is a positive integer. The length of each piece will be:
Length of each piece = 25m / n
If the length of each piece is a rational number (can be expressed as a ratio of two integers), then it is not possible to obtain a piece with an irrational length. However, if the length of each piece is an irrational number (cannot be expressed as a ratio of two integers), then it is possible to obtain a piece with an irrational length.
To determine whether the length of each piece is rational or irrational, we need to check the value of n.
If n is a divisor of 25, then the length of each piece will be a rational number. For example, if n = 1, 5, or 25, the length of each piece will be 25m, 5m, or 1m, respectively, which are all rational numbers.
However, if n is not a divisor of 25, then the length of each piece will be an irrational number. For example, if n = 2 or 3, the length of each piece will be 12.5m or 8.33...m, respectively, both of which are irrational numbers.
Therefore, it is possible to get a piece with an irrational length when cutting a 25m ribbon into equal pieces, as long as the number of pieces is not a divisor of 25.