Math, asked by sree249, 11 months ago

the length of a Diagonals of a rhombus are 24 cm and 32 cm find the sides of is​

Answers

Answered by veerendrakumaruppu
2
Given:

Length of diagonal 1 = 24 cm

Length of diagonal 3 = 32 cm

Diagonals of a Rhombus bisect each other at 90 degrees.

There there are 4 right angle triangles formed with sides 24/2 = 12 cm & 32/2= 16 cm as it sides.

If we find the hypotenuse of one of the triangles using pythagorous theorem is the side of given rhombus, since all sides of rhombus are equal.

12^2 + 16^2 = hypotenuse^2 = (side of rhombus)^2

(side of rhombus)^2 = 12^2 + 16^2

(side of rhombus)^2 = 144 + 256

(side of rhombus)^2 = 400

side of rhombus = sqrt(400) = 20 cm —> Answer

Answered by Anonymous
24

SOLUTION:-

We know that the diagonals of rhombus bisect each other at right angles.

Therefore,

 =  > OA =  \frac{1}{2}  \times 24 = 12cm \\  \\  =  > OB =  \frac{1}{2}  \times 32 = 16cm

In right angle ∆AOB,

 =  > AB =   \sqrt{ {OA}^{2}  +  {OB}^{2} }  \\  \\  =  >  \sqrt{(12) {}^{2} + ( {16)}^{2}  }  \\  \\  =  >  \sqrt{144 + 256}  \\  \\  =  >  \sqrt{400}  \\  \\  =  > 20cm

Therefore,

Sides of rhombus= 20cm

Hope it helps ☺️

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