Question

Abcd is a rectangle aq is one third of ab and p is the mid point of ad if the area of aqcp is 25 area then what is the area of abcd

Answer 1

60 sq units

Step-by-step explanation:

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Answer 2

The area of rectangle ABCD is 60 sq unit

Step-by-step explanation:

ABCD is a rectangle. Q is a point on side AB such that

$AQ=\dfrac{1}{3}AB$

P is a point on side AD such that

$AP=\dfrac{1}{2}AD$

In ΔACD, P is mid point of AD.

If two triangle has same height then their area divide into their base.

$ar(\triangle ACP)=ar(\triangle PCD)$ --------- (1)

In ΔABC, Q is a point on side AB

$AQ=\dfrac{1}{3}AB$

$2ar(\triangle ACQ)=ar(\triangle BCQ)$ ---------- (2)

But ar(ACQ) + ar(ACP) = 25 --------- (3)

3 ar(ACQ)=2 ar(ACP) ------- (4)

So, ar(ACP) = 15

ar(ACQ) = 10

ar(ABCD) = ar(ACP) + ar(ACQ) + ar(BCQ) + ar(PCD)

ar(ABCD) = 15 + 10 + 20 + 15

ar(ABCD) = 60

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