Geometry Problem

Question

The diagonals of a rhombus are 28cm and 54cm long. Find the perimeter of the rhombus.

Answer 1

The diagonals of a rhombus bisect each other,are perpendicular to each other, and divide the rhombus into 4 congruent right triangles.  

 

So, each side, s, of the rhombus is the hypotenuse of a right triangle with legs 14 cm and 27 cm.

 

By the Pythagorean Theorem, s² = 14² + 27²

 

                                          s² = 925    s = √925 = 5√37

 

Perimeter of rhombus = 4s = 20√37.