A chain of designated length 20m is found to be 0.1m too short. Calculate the correct distance when the chain is used to measure a distance of 120m.

March 31, 2026Mathematics

ScanSolve AI Answer

March 31, 2026

Answer

119.4 m

Step 1: Identify the given values. • Measured distance ( $L_m$ ) = $120 \text{ m}$ • Designated length of the chain ( $L$ ) = $20 \text{ m}$ • Error in chain length = $0.1 \text{ m}$ too short

Step 2: Calculate the actual length of the chain ( $L'$ ). Since the chain is $0.1 \text{ m}$ too short, its actual length is: $L' = L - \text{error}$ $L' = 20 m - 0.1 \text{ m}$ $L' = 19.9 \text{ m}$

Step 3: Apply the formula for corrected distance. The formula for the corrected distance ( $L_c$ ) is: $L_c = L_m \times \frac{L'}{L}$

Step 4: Substitute the values and calculate the corrected distance. $L_c = 120 m \times \frac{19.9 m}{20 m}$ $L_c = 120 \times 0.995 \text{ m}$ $L_c = 119.4 \text{ m}$ The correct distance between the two points is: $\boxed{119.4 m}$

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Identify the given values. • Measured distance (L_m) = 120 m • Designated length of the chain (L) = 20 m • Error in chain length = 0.1 m too short Step 2: Calculate the actual length of the chain (L').

Asked on March 31, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 31, 2026

Step 1: Identify the given values. • Measured distance (L_m) = 120 m • Designated length of the chain (L) = 20 m • Error in chain length = 0.1 m too short Step 2: Calculate the actual length of the chain (L'). Since the chain is 0.1 m too short, its actual length is: L' = L - error L' = 20 m - 0.1 m L' = 19.9 m Step 3: Apply the formula for corrected distance. The formula for the corrected distance (L_c) is: L_c = L_m × (L')/(L) Step 4: Substitute the values and calculate the corrected distance. L_c = 120 m × 19.9 m20 m L_c = 120 × 0.995 m L_c = 119.4 m The correct distance between the two points is: 119.4 m

Asked on March 31, 2026Mathematics

ScanSolve AI AnswerAnswered on March 31, 2026

Step 1: Identify the given values. • Measured distance (L_m) = 120 m • Designated length of the chain (L) = 20 m • Error in chain length = 0.1 m too short Step 2: Calculate the actual length of the chain (L'). Since the chain is 0.1 m too short, its actual length is: L' = L - error L' = 20 m - 0.1 m L' = 19.9 m Step 3: Apply the formula for corrected distance. The formula for the corrected distance (L_c) is: L_c = L_m × (L')/(L) Step 4: Substitute the values and calculate the corrected distance. L_c = 120 m × 19.9 m20 m L_c = 120 × 0.995 m L_c = 119.4 m The correct distance between the two points is: 119.4 m