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# Each Side of a Rhombus is 10 Cm. If One of Its Diagonals is 16 Cm Find the Length of the Other Diagonal. - Mathematics

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#### Question

Each side of a rhombus is 10 cm. If one of its diagonals is 16 cm find the length of the other diagonal.

#### Solution We have,

ABCD is a rhombus with side 10 cm and diagonal BD = 16 cm

We know that diagonals of a rhombus bisect each other at 90°

∴ BO = OD = 8 cm

In ΔAOB, by pythagoras theorem

AO2 + BO2 = AB2

⇒ AO2 + 82 = 102

⇒ AO2 = 100 − 64 = 36

⇒ AO = sqrt36 = 6 cm          [By above property]

Hence, AC = 6 + 6 = 12 cm

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 7: Triangles
Ex. 7.7 | Q: 15 | Page no. 120
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 7: Triangles
Ex. 7.7 | Q: 15 | Page no. 120

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Solution Each Side of a Rhombus is 10 Cm. If One of Its Diagonals is 16 Cm Find the Length of the Other Diagonal. Concept: Application of Pythagoras Theorem in Acute Angle and Obtuse Angle.
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