Question

the length of the diagonals of a rhombus is in the ratio 4 ratio 3 if area is 384 CM square find its side

Answer 1

Let the diagonals be 4x and 3x

Area of rhombus =product of diagonals/2

384 =product of diagonals /2

384*2 =4x * 3x

768=12x²

768/12=x²

64=x²

√64=x

8=x

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

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

Then by Pythagoras theorem

Side²=half of first diagonal²+ half of second diagonal ²

Side²=(32/2)²+(24/2)²

Side²=16²+12²

Side²=400

Side =20cm

Answer 2

So its side is 20 cm.