Question

how to find the length of each side of a rhombus if area and diagonals are given
​

Answer 1

To find the value of diagonal we must first recognize some important properties of rhombuses. Since the perimeter and by definition a rhombus has four sides of equal length, each side length of the rhombus is equal to 6. The diagonals of rhombuses also form four right triangles, with hypotenuses equal to the side length of the rhombus and legs equal to one-half the lengths of the diagonals. We can therefore use the Pythagorean Theorem to solve for one-half of the unknown diagonal:

Answer 2

Explanation:

To find the value of diagonal , we must first recognize some important properties of rhombuses. Since the perimeter is of is , and by definition a rhombus has four sides of equal length, each side length of the rhombus is equal to . The diagonals of rhombuses also form four right triangles, with hypotenuses equal to the side length of the rhombus and legs equal to one-half the lengths of the diagonals. We can therefore use the Pythagorean Theorem to solve for one-half of the unknown diagonal:

, where is the rhombus side length, is one-half of the known diagonal, and is one-half of the unknown diagonal. We can therefore solve for :

is therefore equal to . Since represents one-half of the unknown diagonal, we need to multiply by to find the full length of diagonal .