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20 May, 01:30

A pedestrian bridge is 53 meters long. Due to changes in temperature, the bridge may expand or contract by as much as 21 millimeters. Write and solve an absolute-value equation to find the minimum and maximum lengths of the bridge.

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  1. 20 May, 01:57
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    Length of bridge = 53 meters

    Length changes expected due to changes in temperature = expansion or contraction by 21 millimeters (or 0.021 meters)

    Let length of bridge at any given time be 'a'

    As an absolute value equation, the situation can be expressed as:

    ⇒ |a-53| < 0.021

    Solving the equation

    ⇒ - 0.021 < a-53 < 0.021

    ⇒ 53 - 0.021 < a < 53 + 0.021

    ⇒ 52.979 < a < 53.021

    Hence, the minimum length of the bridge can be 52.979 meters and the maximum length of the bridge can be 53.021 meters.
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