The area of a rhombus is 384 cm. sq. and each side is 20 cms. Find its diagonals.

Let the diagonals of a rhombus are 2x and 2y

We know diagonals intersect at 90º A  B

  C   D

ABCD is a rhombus and diagonals intersect at O

Now, in triangle OCD

Using Pythagoras theorem ,

(CD)² = (CO)² + (OD)²

(20)² = x² + y²

 x² + y² = 400

now we have

area of rhombus = ½ *d1 * d2

  384 = ½ *2x *2y

  384 = 2xy

 xy = 384/2

xy = 192

x = 192/y

put this value in eqn (1)

we get

( + y² = 400

 + y² = 400

 = 400

 = 400y²

- 400y²+36864 = 0

- 144y² - 256y² + 36864 = 0

y²(y²-144) – 256(y²-144) = 0

(y²-256) (y²-144)= 0]

(y²-256) = 0

y² = 256

y = 16

 (y²-144) = 0

y² = 144

y = 12

if y = 16

x= 192/16 = 12

also if y =12

x= 192/12

  = 16

Hence

The length of longer diagonal = 2x = 2*16 = 32m

The length of smaller diagonal = 2y = 2*12 = 24m