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In quadrilateral ABCD P is the midpoint of A&B Q is the midpoint of C&B. If DQP forms a triangle. What is the ratio of ar(

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In quadrilateral ABCD P is the midpoint of A&B Q is the midpoint of C&B. If DQP forms a triangle. What is the ratio of ar(ABCD) to ar(DPQ)

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Julia

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2 thoughts on “In quadrilateral ABCD P is the midpoint of A&B Q is the midpoint of C&B. If DQP forms a triangle. What is the ratio of ar(”

  2. Step-by-step explanation:

    Given, ABCD is a parallelogram having P as mid point of AB.

    Join the diagonal AC and PC.

    We know that the diagonal of a parallelogram divides it into two triangles of equal area.

    Therefore, Ar (ABC) = Ar (ADC) = x cm

    2

    (let)

    Also, let area of APC = BPC = y cm

    2

    (let) [Again, the median of a triangle divides a triangle into two triangles of equal area]

    Given, Ar(APCD) = 36 cm

    2

    ⟹Ar(ACD)+Ar(APC)=36

    ⟹x+y=36…(1)

    Again, Ar (ABC) = Ar (ADC)

    or, Ar (ABC) = Ar (APC) + Ar (BPC)

    or, x = y + y

    or, x = 2y …. (2)

    Putting value of x in (1), we get

    2y+y=36

    ⟹y=12cm

    2

    Therefore, x = 24 cm

    2

    Hence, Ar(ABC) = 24 cm

    This is the right answer for your question.

    Reply

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