Maharashtra State BoardSSC (English Medium) 9th Standard
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Diagonals of a Rhombus Are 20 Cm and 21 Cm Respectively, Then Find the Side of Rhombus and Its Perimeter. - Geometry

Sum

Diagonals of a rhombus are 20 cm and 21 cm respectively, then find the side of rhombus and its perimeter.

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Solution

Let ABCD be the rhombus.
AC = 20 cm and BD = 21 cm
We know that the diagonals of a rhombus bisect at right angles.
So, AO = OC = 10 cm
And BO = OD = 10.5 cm

In ΔAOB,

`AO^2 + OB^2 = AB^2`

`=> 10^2 + 10.5 ^2 = AB^2`

`=> 100 + 110.25 = AB^2`

`=> AB^2 = 210.25`

`=> AB = 14.5  "cm" `

Thus, each side of rhombus = 14.5 cm
Perimeter = AB + BC + CD + DA
= 14.5 + 14.5 + 14.5 + 14.5
= 58 cm.

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APPEARS IN

Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board
Chapter 5 Quadrilaterals
Practice Set 5.3 | Q 4 | Page 69
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