Question

The length of the diagonals of a rhombus are 16 cm and 12 cm. The length of the side of the rhombus is

a. 9 cm b. 10 cm c. 8 cm d. 20 cm​

Answer 1

Step-by-step explanation:

option D is correct answer of this question

Answer 2

Given:-

• The length of the diagonals of a rhombus are 16 cm and 12 cm.

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To find:-

• The length of the side of the rhombus.

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Solution:-

We know that,

• the diagonal of rhombus bisect each other at 90°.

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Let,

• ABCD be the rhombus and AC and BD bisect at point O.

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Here,

• AC = 16 cm
• BD = 12 cm

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Therefore,

• $\sf{AO = \dfrac{16}{2} = 8\: cm}$

• $\sf{BO = \dfrac{12}{2} = 6\: cm}$

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★In right angled triangle AOB:-

${\dag}\:{\underline{\boxed{\sf{\purple{Using\: Pythagoras\: theorem}}}}}$

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$\tt\longrightarrow{AB^2 = AO^2 + BO^2}$

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$\tt\longrightarrow{AB^2 = 8^2 + 6^2}$

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$\tt\longrightarrow{AB^2 = 64 + 36}$

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$\tt\longrightarrow{AB^2 = 100}$

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$\tt\longrightarrow{AB = \sqrt{100}}$

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$\sf\longrightarrow{\boxed{\orange{AB = 10\: cm}}}$

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Hence,

• the length of the side of the rhombus is 10 cm.

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Therefore,

• Option (b) is correct.