Question

the length of the diagonals of a rombhus are 12cm and 6cm. Find the length of the sides

Answer 1

The length of the sides would be $3\sqrt{5}$ cm

Step-by-step explanation:

Let ABCD be the given rhombus with AC and BD as the diagonals.

Given that,

Length of diagonal AC = 6 cm

Length of Diagonal BD = 12 cm

To find,

Length fo AB = BC = CD = DA = ?

Procedure:

As we know that

Diagonals of a rhombus bisect each other at 90°

∵ AO $= 6/2 = 3cm$   (O being the center and intersection point of diagonals)

OB $= 12/2 = 6cm$

& ∠ AOB = 90°

Using Pythagoras theorem,

In ΔAOB,

$AB^2 = OA^2 + OB^2$

by putting the values,

$AB^2 = 3^2 + 6^2$

$AB^2 = 9 + 36$

$AB^2 = 45$

$AB =$ $\sqrt{45}$

∵ $AB =$ $3\sqrt{5}$ cm

Thus, each side of the rhombus measures:

AB = BC = CD = DA = $3\sqrt{5}$ cm

Learn more: Rhombus

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