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:
[tex]QR = 4a-1[/tex]
[tex]PS = 2a+9[/tex]
[tex]PQ = 6b[/tex]
[tex]RS = 11b-10[/tex]
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
[tex]QR=PS\\4a+1 = 2a+9\\2a=8\\a=\dfrac{8}{2}=4\\\\\therefore a = 4[/tex]
Similarly,
[tex]PQ=RS\\6b = 11b-10\\5b=10\\\\b=\dfrac{10}{5}=2\\\\\therefore b=2[/tex]
Therefore the values, For a = 4 and b =2 the Quadrilateral PQRS, will be a Parallelogram.
