Question

if diagonals of rhombus 12cm and 16cm. find the leanth of each side​

Answer 1

$\huge{\underline{\underline{\underline{\frak{\pink{question :}}}}}}$

• If the diagonals of rhombus is 12 cm and 16 cm. Find the side of length of each side.

$\huge{\underline{\underline{\underline{\tt{\purple{answer :}}}}}}$

➾ We know that diagonals of a rhombus are perpendicular bisector of each other.

➾ Let the name of diagonals be ABCD

AC = 16 cm.

BD = 12 cm.

➾ let :

∴ AO = 8 cm

BO = 6 cm

and ∠AOB = 90°

➾ In right angled ∠AOB ....

( by Pythagorus theorem)

$(a {b}^{2}) = (a {o}^{2}) + (o {b}^{2} )$

$\: a {b}^{2} = ({8}^{2}) + ( {6}^{2} )$

$= 64 + 36 = 100$

$\: \sqrt{100} = 10$

So answer is 10 cm.

$\huge\pink\star \small \: length \: of \: each \: side \: is \small{\underline{\boxed{\frak{\blue{10 \: cm}}}}}$

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Answer 2

Answer:

$\huge \boxed {\boxed{ \boxed{\mathtt{\red{question :}}}}}$

• If the diagonals of rhombus is 12 cm and 16 cm. Find the side of length of each side.

$\huge{\tt{ \boxed{ \boxed{\purple{answer :}}}}}$

• We know that diagonals of a rhombus are perpendicular bisector of each other.

• Let the name of diagonals be ABCD

AC = 16 cm.

BD = 12 cm.

• let :

$\sf∴ AO = 8 cm$

$\sf \:BO = 6 cm$

$\sf \: and ∠AOB = 90°$

• In right angled ∠AOB .

( by Pythagorus theorem)

$\sf(a {b}^{2}) = (a {o}^{2}) + (o {b}^{2} )$

$\sf a {b}^{2} = ({8}^{2}) + ( {6}^{2} )$

$\sf = 64 + 36 = 100$

$\sf \sqrt{100} = 10$

So answer is 10 cm.

$\sf \: length \: of \: each \: side \: is \small{\underline{\boxed{\frak{\red{10 \: cm}}}}}$