+1438 What is the perimeter, in units, of a rhombus if its area is 120 square units and one diagonal is 10 units?
+128475 The area of a rhombus = product of the diagonals / 2
So
120 = (10) D / 2
120 = 5 D divide both sides by 5
24 = D = the other diagonal
And the diagonals bisect each other......and these bisected diagonals form legs of a right triangle and the side of the rhombus forms the hypotenuse
So....the legs are 10/2 and 24/2 = 5 and 12
And by the Pythagorean Theorem.....
5^2 + 12^2 = side^2
√ [ 5^2 + 12^2 ] = side
√ 169 = side
13 = side
And since there are 4 sides....the perimeter is 4 * 13 = 52 units
