## Diagonal of a rhombus are 20cm and21cm respectively,then find the side of rhombus and its perimeter​

Question

Diagonal of a rhombus are 20cm and21cm respectively,then find the side of rhombus and its perimeter​

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3 months 2021-07-24T13:10:57+00:00 1 Answers 0 views 0

1. ### SOLUT I O N:

i. Let ABCD be the rhombus.

AC = 20 cm, BD = 21 cm

$${\sf{\dfrac{1}{2}\:×\:20\:=\:10\:cm ~~~~~~~~~ (i)}}$$

Also, BO

$${\sf{\dfrac{1}{2}\:×\:20\:=\; \dfrac{21}{2}\:cm ~~~~~~~~~ (ii)}}$$

ii. in ∆AOB, AOB = 90°

AB = AO + BO

$${\sf{AB^2\:=\; \dfrac{841}{4}}}$$

$${\sf{AB\:=\; \sqrt\dfrac{841}{4}\; \bigg[Taking\; square\:root\:of\; both\;sides\bigg]}}$$

$${\sf{\dfrac{29}{2}\:=\:14.5\:cm}}$$

iii. Perimeter of ABCD

Hence,

$$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Proved!}}}}$$

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