Question

The length of a diagonal of a rhombus are 16 cm and 12 cm find the length of each of its size.

Answer 1

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=> Since we know that the diagonals of a rhombus bisect each other

So AC = 12 OA = 6 & OC = 6

BD = 16 OB = 8 & OD = 8

=> By pyathagoras theorem

(AB)^2 = (OA)^2 + (OB)^2

(AB)^2 = 8^2 + 6^2

(AB)^2 = 64 + 36

(AB)^2 = 100

(AB) = 10

So AB = 10 cm

=> And we also know that all sides of a rhombus are equal

AB = BC = CD = DA

=> So the length of each side = 10 cm
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Answer 2

Answer:

$\boxed{10 cm}$

Step-by-step explanation:

Given:

Diagonals of the Rhombus = 12cm and  16cm

To find:

The length of the side of the Rhombus. = ?

For Information:

• In a rhombus, diagonals bisect each other at right angles.

• All sides of the rhombus are equal.

• The sum of two adjacent angles is equal to 180 degrees

Solution:

FROM THE FIGURE,

$AC^{2} = AB^{2} + BC^{2}$

⇒$AC^{2} = 8^{2} + 6^{2}$

⇒$AC^{2} = 64 + 36$

⇒$AC^{2} = 100$

⇒$AC= \sqrt{100}$

⇒AC = 10cm

∴The lengths of side  of the Rhombus =$\boxed{10 cm}$  

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