Question

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Answer 1

Answer:

The Correct Option is C. a =4 , b = 2.

Therefore the values, For a = 4 and b =2 the Quadrilateral PQRS, will be a Parallelogram.

Step-by-step explanation:

Given:

$QR = 4a-1$

$PS = 2a+9$

$PQ = 6b$

$RS = 11b-10$

To Find:

a and b =? for PQRS to be a Parallelogram.

Solution:

For a Parallelogram,

• Opposite sides are parallel.
• Opposite sides are equal.
• Opposite angles are equal.

∴ QR || PS and PQ || SR .....Opposite sides are parallel.

∴  QS = PS and

    PQ = SR       ..............Opposite sides of Parallelogram are equal.

Substituting the values we get

$QR=PS\\4a+1 = 2a+9\\2a=8\\a=\dfrac{8}{2}=4\\\\\therefore a = 4$

Similarly,

$PQ=RS\\6b = 11b-10\\5b=10\\\\b=\dfrac{10}{5}=2\\\\\therefore b=2$

Therefore the values, For a = 4 and b =2 the Quadrilateral PQRS, will be a Parallelogram.