Math, asked by rohit582, 1 year ago

Rhombus of side 30 cm has one of its diagonal 36 cm find the diagonal remember the diagonal of a rhombus are perpendicular to each other

Answers

Answered by sanjeevk28012
9

The measure of other diagonal is 48 cm .

Step-by-step explanation:

Given as :

For Rhombus

The side of Rhombus = s = 30 cm

Measure of one diagonal = d_1 = 36 cm

Let The Measure of other diagonal = d_2 cm

According to question

The diagonal of a rhombus are perpendicular to each other

Since , The diagonal of rhombus bisect each other at right angle

Now,

∵ Side of rhombus = \dfrac{1}{2} × \sqrt{d_1^{2}+d_2^{2}  }

Or,   s =  \dfrac{1}{2} × \sqrt{(36cm)^{2}+d_2^{2}  }

Or, 2 × s = \sqrt{(36cm)^{2}+d_2^{2}  }

Squaring both side

i.e ( 2 s )²  = ( \sqrt{(36cm)^{2}+d_2^{2}  }

Or, ( 36 cm )² + ( d_2 )² = 4 s²

Or, ( 36 cm )² + ( d_2 )² = 4 (30 cm)²

Or, ( d_2 )² = 4 × 900 cm² - 1296 cm²

Or, ( d_2 )² = 3600 cm² - 1296 cm²

∴    ( d_2 )² = 2304 cm²

Or,  d_2 = √2304

i.e d_2 = 48 cm

So, The measure of other diagonal = d_2 = 48 cm

Hence, The measure of other diagonal is 48 cm . Answer

Answered by nidhisoma1812
1

Answer:

The measure of other diagonal is 48 cm .

Step-by-step explanation:

Given as :

For Rhombus

The side of Rhombus = s = 30 cm

Measure of one diagonal =  = 36 cm

Let The Measure of other diagonal =  cm

According to question

The diagonal of a rhombus are perpendicular to each other

Since , The diagonal of rhombus bisect each other at right angle

Now,

∵ Side of rhombus =  ×

Or,   s =   ×

Or, 2 × s =

Squaring both side

i.e ( 2 s )²  = (  )²

Or, ( 36 cm )² + (  )² = 4 s²

Or, ( 36 cm )² + (  )² = 4 (30 cm)²

Or, (  )² = 4 × 900 cm² - 1296 cm²

Or, (  )² = 3600 cm² - 1296 cm²

∴    (  )² = 2304 cm²

Or,   = √2304

i.e  = 48 cm

So, The measure of other diagonal =  = 48 cm

Hence, The measure of other diagonal is 48 cm . Answer

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