Geometry question

Question

If the area of a rhombus is 120 square meter and one of its diagonals is 24 meter, find the length of a side of the rhombus. 

Answer 1

A rhombus is a parallelogram with 4 congruent sides.

 

The area of a rhombus is half of the product of its diagonals.

 

So, since area = 120 and the length of one of the diagonals is 24, then the length of the other diagonal, x, satisfies the equation:

 

    (1/2)(x)(24) = 120

 

            12x = 120

 

               x = 10

 

In a rhombus, the diagonals bisect each other and are perpendicular to each other, so the diagonals divide the rhombus into 4 congruent right triangles.  The legs of each right triangle have lengths 5 and 12, and the hypotenuse of each triangle is a side, s, of the rhombus.

 

By the Pythagorean Theorem, s² = 5²+12²

 

                                         s² = 169

 

                                         s = 13