Question

The length of the diagonals of a rhombus is in the ratio of 4:3.If its area is 384cm2,find its side.

Answer 1

Let the diagonals be 4x and 3x
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As we know that area of rhombus = (product of diagonals)/2

Now, area is given,

384 = (3x*4x)/2

384*2 =12x²

768 =12x²

768/12 =x²

64 =x²

√64 =x

8 =x

Now,

Diagonals are 4*8 = 32cm and 3*8 =24cm


Now,

As we know that diagonals of rhombus bisects each other by 90,

By Pythagoras theorem,

(Half of first diagonal)² +(half of second diagonal)² =side²

(24/2)² +(32/2)² =side²

12² + 16² =side²

144 + 256 =side²

400 =side²

√400 = side

20 = side

Then,

Side of rhombus is 20cm


I hope this will help you


-by ABHAY

Answer 2

Area of rhombus = 1/2 × D1× D2 = 384 cm^2
let D1= 4x D2 = 3x

384 = 1/2*4x*3x
384 = 6x^2
x^2 = 64
x = 8 cm
D1= 32cm
D2 = 24cm
now we know diagonals of rhombus bisect each other at right angle

side^2 = 16^2+12^2

side ^2 = 400
side = 20cm Answer

hope you got this