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CBSE Class 9 Answered

Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. Find the length of the other diagonal and hence find the area of the rhombus.
Asked by Topperlearning User | 17 Aug, 2017, 07:22: AM
answered-by-expert Expert Answer
Diagonals of a rhombus bisect each other at right angles.
Let ABCD be the rhombus, Diagonal AC= 16 cm and side AB = 10 cm.
In right triangle AOB, AB = 10 cm, AO = 8 cm
By Pythagoras theorem, AB2 = AO2 + BO2
(10)2 = (8)2 + BO2
BO2 = (10)2 – (8)2
BO = 6 cm
Diagonal BD = 2 x 6 = 12 cm
Hence length of other diagonal = 12 cm; Area of rhombus = 96 cm2
Answered by | 17 Aug, 2017, 09:22: AM
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