Question

In a trapezium ABCD, AB || CD, P and Q are the mid points of sides AD and BC respectively. If
AB = 3 cm, CD = 9 cm then find the length of PQ (in cm)​

Answer 1

Answer:

6 cm

Step-by-step explanation:

Hope this picture will help you.

Answer 2

The length of PQ=6 cm

Step-by-step explanation:

$AB\parallel CD$

P is the mid point of side AD

Q is the mid point of side BC

AB= 3cm

CD= 9 cm

Let E is the mid-point of AC

In triangle ADC

By mid-segment theorem

$PE\parallel CD$

$PE=\frac{1}{2}CD=\frac{9}{2}$ cm

In triangle ABC

By mid-segment theorem

$EQ\parallel AB$

$EQ=\frac{1}{2}AB=\frac{3}{2}$

PQ=PE+EQ

$PQ=\frac{9}{2}+\frac{3}{2}=\frac{9+3}{2}=6 cm$

Hence, the length of PQ=6 cm

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