Question

the perimeter of rhombus is 20cm and one of its diagonal is 6 cm. find the lenth of other diagonal.​

Answer 1

perimeter of rhombus = 20 cm Let the equal side of the rhombus be k Perimeter of rhombus = 4k That is 4k = 20 k = 20/4 = 5 Therefore the side of rhombus, k = 5 cm Given length of one of the diagonal, AC = 8 cm Recall that the diagonals bisect each other at right angles in a rhombus Thus OA = 4 cm In right ΔAOD By Pythagoras theorem, we have AD2 = OA2 + OD2 52 = 42 + OD2 25 - 16 = OD2 OD2 = 9 OD = 3 cm Length of other diagonal BD = 2 x OD = 2 x 3 cm = 6 cm