Question

The lengths of the two diagonals of a rhombus are16cm and 14cm., then the length of each side of the rhombus is (a) √15cm (b) √28cm (c) √113cm (d) √115cm​

Answer 1

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Diagonals of rhombus are cut each other at 90

o

.

Since d

1

=16and d

2

=12

Therefore, by Pythagoras theorem

a

2

=(

2

d

1

)

2

+(

2

d

2

)

2

⇒ a

2

=8

2

+6

2

⇒ a=

100

=10

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Answer 2

Given : The lengths of the two diagonals of a rhombus are16cm and 14cm.,  

To Find : the length of each side of the rhombus

Solution:

Diagonals of  a rhombus  bisect each other perpendicularly

16/2 = 8 cm

14/2 =  7 cm

Using Pythagorean theorem :

Side of rhombus  = √8² + 7²

= √64 + 49

= √113  cm

= 10.63  cm

the length of each side of the rhombus is​ √113  cm

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