What is the perimeter, in units, of a rhombus if its area is 120 square units and one diagonal is 10 units?

SmartMathMan
Dec 5, 2017

#1**+2 **

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

CPhill
Dec 5, 2017