A rhombus has an area of 108 square units. The lengths of its diagonals have a ratio of 3 to 2. What is the length of the longest diagonal, in units?

Guest Mar 15, 2020

#1**0 **

Let first diagonal = a

Let the 2nd diagonal =b

a / b = 3 / 2.......................(1)

Area of rhombus =[a x b] / 2

108 = [a x b] / 2.................(2)

From (1) above: a =3b / 2

Sub this into (2) above and solve for b.

108 =[3b/2 x b] / 2

108 =3b^2 / 4 Cross multiply

432 =3b^2 Divide both sides by 3

b^2 = 144 Take the square root of both sides.

b = 12 Sub this into (1) above.

**a = 18 - The longer diagonal.**

Guest Mar 15, 2020