Question

one diagonal of a rhombus is greater than other by 4 cm .if the area of the rhombus is 96 cm^ ,find the side of the rhombud?​

Answer 1

Answer:

10 cm

Step-by-step explanation:

Let one diagonal be x, then other diagonal is (x+4)

Area of rhombus = 1/2 x d1 x d2

96. = 1/2 (x) (x+4)

96x2 = x^2 + 4x

192 = x^2 + 4x

x^2 + 4x - 192 =0

On solving this equation by middle term splitting, we will get diagonal.

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

x=12

One diagonal is 12 cm and the other diagonal is 16 cm

Diagonals are perpendicular bisector of each other and we get the right angled triangle. On applying Pythagoras theorem, we have

(side)^2 = (6)^2 + (8)^2

= 36 + 64

= 100

side. = √100

side. = 10 cm

Hope it helps!