Question:
Perimeter of a rhombus is 100cm. Length of its one diagonal is 48cm. Find the length of other diagonal. The ans. is 14cm but i am not getting it. Please help.
Answer:
Given perimeter of the rhombus = 100 cm
Since all sides of the rhombus are equal.
So, the length of each side of the rhombus = 100/4 = 25
In triangle AOB,
∠AOB = 90
From Pythagorus Theorem,
AB2 = AO2 + OB2
=> (25)2 = AO2 + (24)2
=> 625 = AO2 + 576
=> AO2 = 625 - 576
=> AO2 = 49
=> AO = √49
=> AO = 7
Now, OC = AO = 7
So, the length of diagonal AB = AO + OC = 7 + 7 = 14 cm
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