Final answer:
To find the length of the shorter piece, we need to determine the fraction of each piece compared to the original length. With the given fractions, we can set up an equation and solve for x to find the length of the shorter piece. The length of the shorter piece is 0.36 meters or 36 centimeters.
Step-by-step explanation:
To find the length of the shorter piece, we need to determine the fraction of each piece compared to the original length. Let's say the length of the longer piece is x.
So, the length of the shorter piece would be (1 - x).
According to the given fractions, (1 - x) / x = 5/9.
Cross multiplying, we get 9(1 - x) = 5x.
Simplifying, we get 9 - 9x = 5x.
Combining like terms, we have 14x = 9.
Dividing both sides by 14, we find that x = 0.64.
Finally, the length of the shorter piece is (1 - 0.64) = 0.36 meters, which is equivalent to 36 centimeters.