Question

One diagonal of a rhombus is greater than other by 4cm. If the area of rhombus is 96sq.cm then find the sides of rhombus.​

Answer 1

let the first side be x.

the other side be x+4 cm.

area=1/2*d1*d2

=>96=1/2* x (x+4)

=>96*2=x^2+4x

=>x^2+4x-192=0

=>x^2+16x-12x-192=0

=>x(x+16)-12(x+16)=0

so, (x+16)(x-12)=0

then,x=-16 which is not possible

so,x=12cm.

so,1st diagonal=12cm.

2nd diagonal=12+4=16cm.

it's side is s then we half the digonal and it forms the right angled triangle.

so,

=>s^2=6^2+8^2

=>s^2=36+64

=>s^2=100

s=root 100

so,side is 10 cm each.

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