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A rod was cut into three pieces. The lengths of the three pieces are in the ratio 5:3:2. If the shortest is 25cm long, how long was the rod?

Show workings bit by bit

Let x = length of the rod

5:3:2 = 5x:3x:2x

25cm = 2x

2x/2 = x

25cm/2 = x

x = 12.5cm

Therefore, the rod was 12.5cm long.

Did you know?

Did you know that ratios can be used to solve problems involving measurements? In this case, a rod was cut into three pieces in a ratio of 5:3:2. If the shortest piece measures 25cm, we can determine the length of the entire rod. Let's start by assigning a variable to represent the length of the rod. We'll call it "x." According to the ratio, the lengths of the three pieces can be expressed as 5x, 3x, and 2x, respectively. Since we know that the shortest piece is 25cm long, we can set up the equation: 2x = 25 To find the length of the rod, we need to solve for "x." Dividing both sides of the equation by 2 gives us: x = 25/2 This simplifies to: x = 12.5 Therefore, the length of the rod is approximately 12.5 times the shortest piece. Plugging this value back into the original equation, we find that the rod is approximately 62.5cm long. Isn't it fascinating how ratios can help us solve real-life measurement problems?