Question

20. Each side of a rhombus is 10 cm long and one of its diagonals measures
16 cm. Find the length of the other diagonal.​

Answer 1

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GIVEN:-

• Each side of a rhombus us 10cm long

• One of its Diagonal measures 16cm.

TO FIND:-

• Length of the other Diagonal(BD)

Now,

$\textbf{AOB\:is\:Right\:angled\:triangle}$

$\textbf{AB=10cm=Hypotenuse}$

$\textbf{AO=AC/2=8cm}$

$\text{OB=?}$

Using pythogoras theorm,

$(AO)^2+(OB)^2=(AB)^2$

$(8)^2+(OB)^2=100$

$(OB)^2=36$

$OB=6cm$

Atq.

$BD=2OB$

$BD=2×6$

$BD=12cm$

Hence, The other diagonal measures 12cm.

●●EXTRA INFORMATION●●

• Area of Rhombus=Product of Diagonal/2.

• Perimeter of Rhombus= 4×Sides

• The Diagonal of Rhombus bisect each other at Right angled triangle.