Question

The diagonals of a rhombus are 12 cm and 9 cm long.
Calculate the length of one side of the rhombus.​

Answer 1

Answer:

$\huge{\pink{\boxed{\green{\sf{SIDE=7.5cm}}}}}$

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

$\: \: \: \:{ \orange{given}} \\ { \pink{ \boxed{ \green{d1 = 12cm}}}} \\ { \pink{ \boxed{ \green{d2 = 9cm}}}} \\ \\ {\blue{to \: find}} \\ { \purple{ \boxed{ \red{side =? }}}}$

☆ According to given question:

☆ We know the properties of rhombus

$(1) side \: of \: rhombus \: are \: equal \\ (2)diagonals \: bisects \: each \: other \: at \: 90 \degree \\ (3)bisecting \: of \: diagonals \: form \: 4 \: equal \: right \: angled \: triangle \\ (4)diagonals \: are \: unequal$

☆ According to (2) and (3) properties :

$\to {h}^{2} = {p}^{2} + {b}^{2} \\ \to {h}^{2} = ( {6}^{2} ) + ( {4.5})^{2} \\ \to {h}^{2} = 36 + 20.25 \\ \to {h}^{2} =56.25 \\ \to h = \sqrt{56.25} \\ \to h = 7.5cm\\ { \pink{ \boxed{ \green{\therefore side= 7.5cm}}}}$

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