A rope is cut into 3 pieces with the ratio \( 5: 2: 9 \). The shortest piece is 18 cm . What wos the original length of the rope?

The lengths of the pieces can be represented by the ratios 5x, 2x, and 9x. Given that the shortest piece (2x) is 18 cm, we can set up the equation: \[ 2x = 18 \implies x = 9 \] Now we find the lengths of each piece: - First piece: \( 5x = 5(9) = 45 \) cm - Second piece: \( 2x = 18 \) cm - Third piece: \( 9x = 9(9) = 81 \) cm To find the original length of the rope, we sum the lengths of all the pieces: \[ 45 + 18 + 81 = 144 \] cm. Thus, the original length of the rope was \( 144 \) cm. --- Did you know that ancient cultures often used ropes made from natural fibers, and their lengths could be based on ratios similar to what we see in our problem? For instance, the Egyptians used ropes in constructing pyramids, ensuring they maintained precise measurements through ratios to enhance the structural integrity! When solving ratio problems, a common mistake is forgetting to express the pieces in terms of a common variable, as we did with \( x \). Always double-check the foundational ratios before diving into calculations! An organized approach can save a lot of time.