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    Question

    In the given figure, AB ∥ QP, AB = x, PQ = x + 10, RB

    = x/2, BP = x + 1. Find PQ.
    A 13 units Correct Answer Incorrect Answer
    B 4 units Correct Answer Incorrect Answer
    C 18 units Correct Answer Incorrect Answer
    D 12 units Correct Answer Incorrect Answer

    Solution

    ATQ,

    Given: AB∥PQ, so we use the Basic Proportionality Theorem:

    Substituting values:

    Multiply by 2 to remove the fraction:

    2x(x+1)=x(x+10) Expand and simplify: x2 −8x=0 Factorize = (x−8)=0 Solve for x: x = 8 (since x=0 is not valid) Find PQ: PQ = x+10 = 8+10 = 18

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