If the diagonals of a rhombus are 10 cm and 24 cm in length respectively, find the length of each side of the rhombus.
Answers
Answer:
Thank you for this nice question first of all.
AS we know that diagonals of rhombus bisect each other and they also form a right angle triangle in each part so in a rhombus there ARE FOUR right angle triangle. if we imagine the SIDES of triangles will be half of diagonals.
AS we know that diagonals of rhombus bisect each other so the one side of the triangle will be 5cm and other will be 12 CM of course.
so by Pythagoras theorem, the length of one side of the rhombus will be under root 5 square + 12 square which will come to 13 sold each side of the rhombus is 13 cm
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Diagonals of rhombus are perpendicular bisector so.
In ∆AOB
AO = 24/2
AO = 12
and
BO = 10/2
BO = 5
By phythagores theorem
AB² = BO² + AO²
AB² = 5² + 12²
AB² = 25 + 144
AB² = 169
AB = √169
AB = 13
so AB=BC=CD=AD = 13 .... Side of a rhombus