Question

The diagonals of a rhombus measure
16cm and 30cm. Find its perimeter.​

Answer 1

Answer:

d1xd2=16x20

320

Step-by-step explanation:

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Answer 2

Answer :-

• 68cm

• Given :

• Diagonals of the rhombus = 16cm and 30cm

• To Find :

• Perimeter of the rhombus

• Solution :

• Let ABCD be a rhombus and its diagonals, AC and BD, are intersecting each other at point O.

• We know diagonals of a rhombus are perpendicular therefore they bisect each other at 90°

So,

$</p><p> \red{\implies \bf{}AO=\dfrac{AC}{2}}$

$\pink{\bf{}\implies \dfrac{16}{2}}$

$\gray{\rm{}\therefore 8}$

$\orange{\implies \sf{}BO=\dfrac{BD}{2}</p><p>}$

$\pink{\bf{}\implies \dfrac{30}{2}}$

$\bold{}\therefore 15$

• By applying Pythagoras theorem in ΔAOB,

$\red{\sf{}\implies OA^2+OB^2=AB^2}$

$\rm{}\implies 8^2+15^2=AB^2</p><p>$

$\green{\bf{}\implies64+225=AB^2}$

$\blue{\sf{}\implies 289=AB^2}$

$\gray{\bf{}\implies AB=\sqrt{289}}$

• Length of the side of rhombus is 17 cm.

• We know,

• All sides of the rhombus are equal.

• Perimeter of rhombus,

• = 4 × Side of the rhombus

• = (4 × 17)cm

• = 68 cm

• Therefore,the perimeter of the given rhombus is equal to to 68cm