Find the values of `PQ` and `QR`

In Fig. 5.3, four line segments PQ, QR, RS and ST are making the letter W, PQ||RS and QR||ST. If angle between PQ and QR is 39^(@) , find the values of x and y.

Find the value of x such that PQ = QR, where P, Q and R are (6,- 1), (1, 3) and (x, 8) respectively.

Find the value of x such that PQ=QR where the coordinates of P,Q and R are (6,-1),(1,3) and (x,8) respectively.

In DeltaPQR, angleQ=90^(@) . If angleP=alpha, angleR=beta, PQ=3 and QR=4 , then find the value of tan beta .

In Delta PQR ,PQ =PR . A is a point in PQ and B is a point in PR , so that QR = RA = AB = BP Find the vlaue of angle Q.

In DeltaPQR, angleR= angleP and QR = 4 cm and PR = 5 cm . Then find the value of length of PQ xx QR xx PR .

In a rhombus PQRS , PR and QR are the diagonals of the rhombus. If PQ=10 cm , then find the value of PR^2+QS^2 .