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

SmartMathMan
Dec 7, 2017

edited by
Guest
Dec 7, 2017

#1**+2 **

Area = product of the diagonals / 2

120 = D * 10 / 2

120 = D * 5

24 = D = the other diagonal length

And the diagonals bisect each other...so 1/2 of each of their lenghts will form legs of a right triangle with the side asa hypotenuse.....so we have that

5^2 + 12^2 = side^2

169 = side ^2 take the square root of each side

13 = side

And the perimeter is 4 times this = 52

CPhill
Dec 7, 2017