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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.

Mathematics

ScanSolve AI Answer

Answer

119.4 m\text{119.4 m}

Step-by-step solution

4 steps
  1. Identify the given values.

    • Measured distance (LmL_m) = 120 m120 \text{ m}
    • Designated length of the chain (LL) = 20 m20 \text{ m}
    • Error in chain length = 0.1 m0.1 \text{ m} too short
  2. Calculate the actual length of the chain (L′L').

    Since the chain is 0.1 m0.1 \text{ m} too short, its actual length is:

    L′=L−errorL' = L - \text{error} L′=20 m−0.1 mL' = 20 \text{ m} - 0.1 \text{ m} L′=19.9 mL' = 19.9 \text{ m}
  3. Apply the formula for corrected distance.

    The formula for the corrected distance (LcL_c) is:

    Lc=Lm×L′LL_c = L_m \times \frac{L'}{L}
  4. Substitute the values and calculate the corrected distance.

    Lc=120 m×19.9 m20 mL_c = 120 \text{ m} \times \frac{19.9 \text{ m}}{20 \text{ m}} Lc=120×0.995 mL_c = 120 \times 0.995 \text{ m} Lc=119.4 mL_c = 119.4 \text{ m}

    The correct distance between the two points is:

    119.4 m\text{119.4 m}
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