Question

The area of a Rhombus is 60cm² and one of its diagonals is 15cm, then the length of other diagonal is

Answer 1

The area of a rhombus is give by 1/2 times the product of the diagonals. Therefore:

60cm2=12(d1⋅d2)

where d1 and d2 are the diagonals. Letting d1=15cm and solving for d2 gives d2=8cm.

The two diagonals bisect each other and are perpendicular to each other. Therefore the four triangles created by the diagonals in the rhombus are right triangles. Using the Pythagorean theorem on any of these triangles yields that the sides s of the rhombus are given by

(152 ) 2 + (82)2 = s 2

or s = 172cm.

The perimeter is therefore 4 X 172 = 34 cm.