Question

Area of a rhombus is 216 cm and one of its diagonals is 24 cm. the length of the other diagonal is 18 cm . find the sides of the rhombus​

Answer 1

the answer is 15.

Area of rhombus=216 cm²

½ × A × B = 216

12 × B = 216

B = 18 cm

Since diagonals bisect each other at right angles,

therefore,

Side =

$\sqrt{ {12}^{2} } + \sqrt{ {9}^{2} } = 15 cm$

Answer 2

Answer:

The length of the sides of the rhombus is 15 cm.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

In figure, □ABCD is a rhombus.

Diagonals AC & BD intersect each other at point O.

AC = 24 cm

BD = 18 cm

We have to find the lengths of the sides of the rhombus.

Now, we know that,

Diagonals of a rhombus bisect each other.

∴ AO = OC = ½ * AC

⇒ AO = ½ * AC

⇒ AO = ½ * 24

⇒ AO = 12 cm - - ( 1 )

Also,

BO = OD = ½ * BD

⇒ OD = ½ * BD

⇒ OD = ½ * 18

⇒ OD = 9 cm - - ( 2 )

Now, we know that,

Diagonals of a rhombus are perpendicular bisectors of each other.

∴ In △AOD, m∟AOD = 90°,

∴ ( AD )² = ( AO )² + ( OD )² - - - [ Pythagoras theorem ]

⇒ AD² = ( 12 )² + ( 9 )² - - - [ From ( 1 ) & ( 2 ) ]

⇒ AD² = 144 + 81

⇒ AD² = 225

⇒ AD = √225 - - - [ Taking square roots ]

⇒ AD = 15 cm

All sides of a rhombus are congruent.

∴ AB = BC = CD = AD = 15 cm

∴ The length of the sides of the rhombus is 15 cm.