The diagonals of a parallelogram qrst, tr and qs, intersect at point u, if rs = 10 , st=12,and ru=9.5 , find the perimeter of the parallelogram qrst.

a. 39
b. 44
c. 88
d.100

(B)44

Step-by-step explanation:

It is given that The diagonals of a parallelogram QRST, TR And QS, Intersect at point U, if RS = 10 , ST=12,And RU=9.5.

Now, Since, RS =10, then RS=QT=10 (Opposite sides of parallelogram are equal).

And, ST=12, then ST=QR=12 (Opposite sides of parallelogram are equal)

Thus, The perimeter of the parallelogram QRST is given as:

Perimeter=Sum of all the sides

Perimeter=QR+RS+ST+TQ

Perimeter=12+10+12+10

Perimeter=44

Therefore, the perimeter of the given parallelogram QRST is 44 units.

Hence, option B is correct.

I found a similar question with a corresponding figure. I'll attach the image.

There are 2 isosceles triangle.

1st and 2nd side: 20 ; 3rd side: 35
1st and 2nd side: 44 ; 3rd side: x

20/35 = 44/x

Cross multiply
20x = 44*35
20x = 1,540
x = 1,540/20
x = 77