The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter. - Mathematics

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Sum

The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.

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Solution

Let ABCD be a rhombus (all sides are of equal length) and its diagonals, AC and BD, are intersecting each other at point O. Diagonals in a rhombus bisect each other at 90°. It can be observed that

`AO = (AC)/2 = 16/2 = 8` cm

`BO = (BD)/2 = 30/2 = 15` cm`

By applying Pythagoras theorem in ΔAOB,

OA2 + OB2 = AB2

82 + 152 = AB2

64 + 225 = AB2

289 = AB2

AB = 17

Therefore, the length of the side of rhombus is 17 cm.

Perimeter of rhombus = 4 × Side of the rhombus = 4 × 17 = 68 cm

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Chapter 6: The Triangle and its Properties - Exercise 6.5 [Page 130]

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NCERT Mathematics Class 7
Chapter 6 The Triangle and its Properties
Exercise 6.5 | Q 8 | Page 130

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