oints Q and R are midpoints of the sides of triangle ABC. Triangle A B C is cut by line segment Q R. Point Q is the midpoint of

Question

oints Q and R are midpoints of the sides of triangle ABC.

Triangle A B C is cut by line segment Q R. Point Q is the midpoint of side A B and point R is the midpoint of side A C. The lengths of A Q and Q B are 4 p, the length of Q R is 2 p + 3, and the length of C B is 6 p minus 4. The lengths of A R and R C are congruent.

What is AQ?

10 units
14 units
20 units
32 units

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Arya 15 hours 2021-09-15T08:44:39+00:00 1 Answer 0

Answers ( )

    0
    2021-09-15T08:46:03+00:00

    Answer:

    AQ = 20 units

    Step-by-step explanation:

    Comparing triangle AQR to ABC,

    \frac{AQ}{AB} = \frac{QR}{BC}

    \frac{4p}{8p} = \frac{2p + 3}{6p-4}

    cross multiply and make p the subject of formula, we have:

    8p (2p+3) = 4p(6p-4)

    16p^{2} + 24p = 24p^{2} – 16p

    24p + 16p = 24p^{2} – 16p^{2}

    40p = 8p^{2}

    divide through by 8p,

    p = 5

    Therefore, AQ = 4p

                            = 4 × 5

                            = 20

    AQ = 20 units

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45:7+7-4:2-5:5*4+35:2 =? ( )