Question

The diagonals of a rhombus are in the ratio 2:3.If the area of a rhombus is 48 cm
Find the lengths of the both the diagonals​

Answer 1

Step-by-step explanation:

Let the diagonals be 2k and 3k.

The Area = (1/2) * product of diagonals = 3k^2

3k^2 = 390625; k= 625 / sqrt(3)

Since the diagonals of a rhombus bisect each other perpendicularly, one side of the rhombus forms the hypotenuse of a right triangle with sides equal to (1/2) the diagonals.

so a side is given by sqrt(((1/2)(2k))^2+((1/2)(3k))^2)

=sqrt(k^2+(9/4)k^2)=sqrt((13/4)k^2)=sqrt(13/4)k.

perimeter = 4*sqrt(13)*k/sqrt(4)=2*sqrt(13)*k

= 2*sqrt(13)*625/sqrt(3)=1250*sqrt(13)/sqrt(3)

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