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Question

If diagonals of a rhombus are 10cm and 24cm, find its perimeter.


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Solution

Step 1: Given is a rhombus.

The diagonals AC and BD are of length 10cm and 24cm respectively.

Step 2: Find the lengths of OB and OC.

The diagonals of a rhombus bisect each other at right angles.

OB=12(BD)ā‡’OB=12(24)=12

OC=12(AC)ā‡’OC=12(10)=5

Step 3: Find the length of BC.

Use the Pythagoras theorem, to find the length of BC.

(BC)2=(OB)2+(OC)2ā‡’(BC)2=122+52ā‡’(BC)2=144+25ā‡’(BC)2=169ā‡’BC=13(Squarerootof169is13)

Step 4: Find the perimeter of rhombus.

All the four sides of a rhombus are equal.

Perimeter=4Ɨside=4ƗBC=4Ɨ13=52

Therefore, the perimeter of the rhombus with diagonals 10cm and 24cm is 52cm.


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