Question

If the area of a rhombus is 135sqcm and one of its diagonal is 18cm find the length of the other diagonal​

Answer 1

Given :

• Area of Rhombus is 135 cm² .
• Length of one diagonal of the rhombus is 18 cm .

To Find :

• Length of other Diagonal .

Solution :

$\longmapsto\tt{Diagonal\:1\:({d}_{1})=18\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rhombus=\dfrac{1}{2}\times{{d}_{1}}\times{{d}_{2}}}$

Putting Values :

$\longmapsto\tt{135=\dfrac{1}{{\cancel{2}}}\times{{\cancel{18}}}\times{{d}_{2}}}$

$\longmapsto\tt{135=9\:{d}_{2}}$

$\longmapsto\tt{\cancel\dfrac{135}{9}={d}_{2}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\pink{{d}_{2}}\blue{=}\green{15\:cm}}}$

So , The Length of other diagonal is 15 cm .

VERIFICATION :

$\longmapsto\tt{135=\dfrac{1}{{\cancel{2}}}\times{{\cancel{18}}}\times{15}}}$

$\longmapsto\tt{135=9\times{15}}$

$\longmapsto\tt\bf{135=135}$

HENCE VERIFIED

Answer 2

Answer:

15 cm is the length of the other diagonal.

Step-by-step explanation:

Given :

=> Area of rhombus = 135 cm²

=> First diagonal length = 18 cm

To find :

=> Second diagonal length

Solution :

>> Area of rhombus:

=> 1/2 × d1 × d2

=> 1/2 × 18 × d2 = 135

=> 9 × d2 = 135

=> d2 = 135/9

∴ d2 = 15 cm

• Hence, the length of second diagonal is 15 cm.

Verification:

=> 1/2 × d1 × d2 = 135

=> 1/2 × 18 × 15 = 135

=> 9 × 15 = 135

=> 135 = 135

∴ L.H.S = R.H.S