An architect is sketching a blueprint of a patio for a new fence. On the blueprint, C is the midpoint of segment AD. Point B is the midpoint

Question

An architect is sketching a blueprint of a patio for a new fence. On the blueprint, C is the midpoint of segment AD. Point B is the midpoint of segment AC. If BC = 8 feet, what is the length of AD?

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Valentina 2 weeks 2021-09-12T09:22:40+00:00 1 Answer 0

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    2021-09-12T09:23:46+00:00

    Answer:

    The length of AD is 32 feet

    Step-by-step explanation:

    Proportional distances

    When distances are proportions of others, we can express all of them as relative fractions until we reach some known distance and solve for the desired length

    Let’s call x the length of AD. Given C is the midpoint of AD, then

    \displaystyle AC=CD=\frac{x}{2}

    Given B is the midpoint of AC, then

    \displaystyle AB=BC=\frac{AC}{2}=\frac{x}{4}

    If we know BC=8 feet

    \displaystyle \frac{x}{4}=8\ feet

    \displaystyle x=32\ feet

    The length of AD is 32 feet

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