Question

the perimeter of a rhombus is 40 cm of the ratio of its diagonal is 3:4 then the length of the diagonal will be ? ( please step by step explanation)​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

To find : length of diagonal of rhombus

Given : Perimeter of rhombus $= 40 \ cm$

            Ratio of its diagonal is $3 :4$

Solution :

• We  know that , all sides of rhombus  are equal .Therefore , let a be the side of rhombus.
• $d_{1}$ and $d_{2}$ be the diagonals of rhombus .
• Then , perimeter = $4a$

                          $40\ cm = 4a \\a = 10 \ cm$

• Ratio of its diagonal is $3 :4$

             $\frac{d_{1} }{d_{2} } =\frac{3}{4}$  

             $d_{1} = \frac{3d_{2} }{4}$  ---------------(i)

             $a^{2} = \frac{d_{1} ^{2} }{4} + \frac{d_{2} ^{2} }{4}$

             $d_{1} ^{2} + d_{2} ^{2} = 4a^{2}$

             $\frac{9d_{2} ^{2} }{16} + d_{2} ^{2} = 4a^{2} \\\frac{25d_{2} ^{2} }{16} = 400$

       Squaring both the sides  

               $\frac{5d_{2} ^{2} }{4} = 20$

                $d_{2} = 16$

         Put $d_{2} = 16$  in (i)

              $d_{1} =12$

Hence , length of diagonals is $12\ cm$ and $16\ cm$.

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