Question

the diagonals of a rombhus measure 16cm diagonal of and 30cm then find its perimeter ​

Answer 1

• The perimeter of the rhombus is 68 cm

Given:

The diagonals of the rhombus ABCD is diagonal 1 (AC) = 30 cm and diagonal 2 (BD) = 16 cm

To find:

The perimeter of the rhombus

From the attached image we get ABCD rhombus,

Some Properties of a rhombus,

• All the sides of the rhombus are equal.
• The diagonals of the rhombus are perpendicular to each other.
• The diagonals bisect each other.

So,

AO = OC = 1/2 AC = 15 cm each

BO = DO = 1/2 BD = 8 cm each

We get four right-angled triangles,

ΔAOB, ΔBOC, ΔCOD, ΔDOA

We can take any triangle,

ΔAOB, right angles at O

⇒ (AO)² + (BO)² = (AB)²

⇒ (15)² + (8)² = (AB)²

⇒ 225 +  64 = (AB)²

⇒ 289 = (AB)²

⇒ 17 = AB

[By taking square roots in both the sides]

Now,

As all the sides are equal so,

AB = BC = DC = AD = 17 cm each

The perimeter of the rhombus

= 4 * (side)

= 4 * 17

= 68 cm

Answer 2

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The diagonals of a rombhus measure 16cm diagonal of and 30cm then find its perimeter

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P=4a

a = √p² + q²/2

Solving for P

P = 2√p² + q²

= 2.√16² + 30²

= 68cm