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If Perimeter of a Rhombus is 100 Cm and Length of One Diagonal is 48 Cm, What is the Area of the Quadrilateral ? - SSC (English Medium) Class 8 - Mathematics

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Question

If perimeter of a rhombus is 100 cm and length of one diagonal is 48 cm, what is the area of the quadrilateral ?

Solution

Perimeter of the rhombus = 100 cm

⇒ `4 xx` side = 100

⇒ side = `100/4` = 25cm 

Thus, each side of the rhombus = 25 cm.
Diagonals of a rhombus bisect each other at 90°
So, AO = OC = `48/2` = 24 cm

In Δ AOB 

We apply Pythagoras theorem,

AO² + OB² = AB²

⇒ 24²  + OB²  = 25² 

⇒ OB²  = 625 - 576 = 49

⇒ OB = 7 cm 

So, DB = `2 xx "OB" = 2 xx 7` = 14 cm

Area of rhombus = `1/2 xx` (product of diagnols) = `1/2 xx 14 xx 48` = 336 cm²

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 15: Area
Practice Set 15.2 | Q: 3 | Page no. 97
Solution If Perimeter of a Rhombus is 100 Cm and Length of One Diagonal is 48 Cm, What is the Area of the Quadrilateral ? Concept: Area of a Rhombus.
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