Question:
A piece of string is 40 cm long. It is cut into three pieces. The longest piece is three times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece.
A piece of string is 40 cm long. It is cut into three pieces. The longest piece is three times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece.
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Use algebraic equations to express the relationship between the parts and solve for unknowns.
Updated On: Aug 4, 2025
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The Correct Option is D
Solution and Explanation
Let the length of the shortest piece be \( x \).
- The length of the middle-sized piece is \( 3x \).
- The length of the longest piece is \( 3 \times 3x = 9x \).
The total length of the string is 40 cm, so:
\[
x + 3x + 9x = 40.
\]
Simplifying:
\[
13x = 40 \Rightarrow x = \frac{40}{13} \approx 9.
\]
Thus, the length of the shortest piece is 9 cm.
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