Question

The sides of a rhombus are 5 cm each and one diagonal is 8 cm. Calculate the length of the other diagonal and the area of the rhombus.
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Answer 1

Step-by-step explanation:

Diagonals bisect each other and they are perpendicular in rhombus

Let half the length of second diagonal be x

As two diagonals and a side form right angled triangle ;

⇒x

2

+4

2

=5

2

⇒x=3

⇒length of 2nd side =2x=6cm

Area of rhombus =

2

1

d

1

d

2

=

2

1

×8×6

=24cm

2

Answer 2

Answer:

The sides of a rhombus are 5 cm each and one diagonal is 8 cm. The length of the other diagonal is 6 cm and the area of the rhombus is 24 sq. cm.

Step-by-step explanation:

Diagonals bisect each other and they are perpendicular in rhombus

Let half the length of the second diagonal be x

As two diagonals and a side form right-angled triangle ;

⇒ $x^2 +4^2 =5^2$

⇒ $x^2 + 16 = 25$

⇒ $x^2 = 25 - 16$

⇒ $x^2 = 9$

⇒x=3

⇒length of 2nd side =2x = 2(3)=6cm

Area of rhombus $=\frac{1}{2} d_1d_2$

$= \frac{1}{2} \times 8 \times 6$

=24 sq. cm

So, the area of rhombus is 24 sq. cm.