The Diagonals of a quadrilateral are of lengths 10cm and 24cm. If the diagonals bisects each other at right angles, find the length of each side of the quadrilateral. What special names do we give to this quadrilateral?
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as the diagonals bisect each other at 90 we will use pythagoras theorem . here the base and other side will be the diagonals divided by 2 ( as the bisections of the diagonals are forming the triangle) and according to pythagoras theorem -
hypooteneuse2 = base2 + verical2
side2 = (10/2)2 + ( 24/2 )2
side2 = 52 + 122
side2 = 25+ 144
side2 = 169
side = 13cm
and in all the rest 3 triangles the vertical and base are going to be same thus all the sides are same.
the special name given to such a quadrilateral is a rhombus
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