Math, asked by monisha200905, 1 month ago

the area of a rhombus is 100sq CM and length of one of its diagonalis 8cm find the length of the other diagonali​

Answers

Answered by TwilightShine
9

Answer -

  • The length of the other diagonal = 25 cm.

To find -

  • The length of the other diagonal.

Step-by-step explanation -

  • Here, the area of a rhombus and the length of one of it's diagonals is given to us. We have to find the length of it's other diagonal.

Let -

  • The length of the other diagonal be "x" cm.

We know that -

 \underline{\boxed{\sf Area_{(rhombus)} = \dfrac{1}{2} \times d_1 \times d_2}}

Where -

  • d₁ = Diagonal 1.
  • d₂ = Diagonal 2.

Here -

  • One of the diagonals of the rhombus measures 8 cm.

  • The area of the rhombus is 100 cm².

Therefore -

  \bf\longmapsto 100 =  \dfrac{1}{2}  \times 8 \times x

 \longmapsto \bf100 =  \dfrac{1}{2}  \times 8x

 \longmapsto \bf100 =  \dfrac{8x}{2}

 \longmapsto \bf100 \times 2 = 8x

 \longmapsto \bf 200 = 8x

 \longmapsto \bf   \cancel{\dfrac{200}{8}} = x

 \longmapsto \bf25 \: cm = x

 \\

Hence -

  • The length of the other diagonal of the rhombus is 25 cm.

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