Diagonal of a quadrilateral are of length 10 cm and 24 cm. if the diagonal bisects each other at right angle, find the length of each sides of a quadrilateral . what special name can you give to this quadrilateral.
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Let the quadrilateral be ABCD and its diagonals be AC = 24cm and BD = 10cm, meeting at O.
Given that AO = OC = 12cm
BO = OD =5cm
In triangle AOB, angle O is 90
So, using pythagoras theorem,
AO^2 + BO^2 = AB^2
12^2 + 5^2 = AB^2
144+25 = AB^2
169 = AB^2
13^2 = AB^2
AB = 13cm
Similarly in triangle BOC, COD and DOA, we get BC = CD = AD = 13cm
As all sides are equal and diagonals bisect each other at 90, the quadrilateral is a RHOMBUS.
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