Question

the lengths of the diagonal of a rhombus are 16cm and 12cm respectively. find the length of each of its sides.

Answer 1

Heya !!




Let ABCD is a rhombus in which AD and BC are it's two diagonals.





Let AC = 16 cm and BD = 12 cm




Therefore,



OA = 1/2 × AC = 1/2 × 16 = 8 cm



And,




OB = 1/2 × BD = 1/2 × 12 = 6 cm






In right angle triangle OAB,




OA = 8 cm and OB = 6 cm



To find :- Length of side AB.





By Pythagoras theroem ,



( H )² = (B)² + (P)²


( AB)² = (OB)² + (OA)²




(AB)² = (6)² + (8)²




(AB)² = 36 + 64






(AB)² = 100




AB = root 100 = 10 cm



Hence,



Side of rhombus ABCD = AB = AC = BD = CD = 10 cm.