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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?

 Mar 15, 2020
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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.

 Mar 15, 2020

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