the length of each side of the rhombus pqrs is 15cm if diagonal pr=24cm find the length of the other - Maths - Areas of Parallelograms and Triangles

Question

the length of each side of the rhombus pqrs is 15cm if diagonal
pr=24cm find the length of the other diagonal qs

Manbar Singh · Accepted Answer

We have, PQRS as the given rhombus, inwhich diagonals PR and QS intersect at O
Now, we know that diagonals of rhombus bisect each other at right angles, then∠POQ = ∠QOR = ∠ROS = ∠SOP = 90°and  OP = OR = PR2 = 242 = 12 cmOS = QQ = QS2Now, In ∆POQ,PQ2 = OP2 + OQ2   Pythagoras theorem⇒ OQ2 = 152 - 122 ⇒ OQ2 = 225 - 144⇒OQ2 =81⇒OQ = 9 cmNow, QS = 2OQ = 18 cm

the length of each side of the rhombus pqrs is 15cm if diagonal pr=24cm find the length of the other diagonal qs