Question

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

Answer 1

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

Answer 2

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 ☺️