Question

lengths of diagonals of a rhombus abcd are 16 cm and 12 cm.find the side and perimeter of rhombus.

Answer 1

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Answer 2

Answer:

$\boxed{40cm}$  

Step-by-step explanation:

Given:

Diagonals of the Rhombus = 12cm and  16cm

To find:

Perimeter 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 =  $\boxed{10cm}$

Perimeter of Rhombus = 4 × Side

                                   = 4 ×  10cm

                                   = $\boxed{40cm}$  

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