Question

I really need help ​

Answer 1

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.

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=(8)/(2)=4\\\\\therefore a = 4`

Similarly,

`PQ=RS\\6b = 11b-10\\5b=10\\\\b=(10)/(5)=2\\\\\therefore b=2`

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