Question

PQRS is Parallelogram whose diagonals intersect each other at right angles. if the length of the diagonals is 10 cm and 12 cm , find the length of all sides of the Parallelogram.​

Answer 1

Answer:

The length of each side of the parallelogram is root over 61 cm , that is 7.81025 cm.

Step-by-step explanation:

Let PQRS is the parallelogram and PR = 10 cm and QS = 12 cm are its two diagonals which intersect each other at O at right angles. Therefore, POQ and QOR are two right angle triangles.

   Here, PO = OR = 5 cm (∵ PO + OR = PR & PO=OR) ,

             OQ = 6 cm (∵ QO + OS = QS & QO = OS)

             ∠POQ = ∠QOR = 90°

For POQ triangle, $PO^{2} +OQ^{2} = PQ^{2}$

                         ⇒ PQ = √(25+36) = √(61) = 7.81025 cm

For QOR triangle, $QO^{2} +OR^{2} = QR^{2}$

                          ⇒QR = √(36+25) = √(61) = 7.81025 cm

Since, PQRS is a parallelogram, PS = QR = √(61) and PQ = SR = √(61)