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Lengths of Diagonals of a Rhombus Abcd Are 16 Cm and 12 Cm. Find the Side and Perimeter of the Rhombus. - SSC (English Medium) Class 8 - Mathematics

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Question

Lengths of diagonals of a rhombus ABCD are 16 cm and 12 cm. Find the side and perimeter of the rhombus.

Solution

ABCD is a rhombus.

Here, segment AC and segment BD are the diagonals of the rhombus ABCD.

l(AC) = 16 cm and l(BD) = 12 cm.

Diagonals of a rhombus are perpendicular bisectors of each other.

∴ m∠AOD = 90º

Also, l(OA) = \[\frac{1}{2}\]l(AC) = \[\frac{1}{2}\]× 16 = 8 cm

l(OD) = \[\frac{1}{2}\]l(BD) =  `1/2`× 12 = 6 cm

In right ∆AOD, 

l(AD)2 = l(OA)+ l(OD)2               (Pythagoras theorem)

⇒ l(AD)= (8)2 + (6)2 

⇒ l(AD)= 64 + 36 = 100

⇒ l(AD) = \[\sqrt{100}\]= 10 cm

All sides of a rhombus are equal.

∴ Perimeter of the rhombus ABCD = 4 × Side of a rhombus = 4 × 10 = 40 cm

Thus, the side and perimeter of the rhombus are 10 cm and 40 cm, respectively.

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 8: Quadrilateral : Constructions and Types
Practice Set 8.2 | Q: 5 | Page no. 47
Solution Lengths of Diagonals of a Rhombus Abcd Are 16 Cm and 12 Cm. Find the Side and Perimeter of the Rhombus. Concept: Some Special Parallelograms - Concept of Rhombus.
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