Maharashtra State BoardSSC (English Medium) 8th Standard
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If Length of a Diagonal of a Rhombus is 30 Cm and Its Area is 240 Sq Cm, Find Its Perimeter. - Mathematics

Sum

If length of a diagonal of a rhombus is 30 cm and its area is 240 sq cm, find its perimeter.

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Solution

Let the other diagonal be d cm
Area of a rhombus = `1/2` (product of diagnols)

⇒ 240 = `1/2 xx` (30 x d)

⇒ d = `(240 xx 2)/30` = 16

AC = 30 cm
DB = 16 cm
Diagonals of a rhombus bisect at right angles. 
In Δ AOB,

AO² + OB² = AB²

⇒ 15² + 8² = AB²

⇒ AB² = 225 + 64 = 289

⇒ AB = √289 = 17 cm

Thus, the side of the rhombus = 17 cm
Perimeter = `4 xx 17` = 68 cm

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APPEARS IN

Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 15 Area
Practice Set 15.2 | Q 4 | Page 97
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