Question

The diagonals of a quadrilateral are of lengths 6 cm and 8 cm. If the diagonals bisect each other at right angles, what is the length of each side of the quadrilateral?

Answer 1

\[\text{ Let the given quadrilateral be ABCD in which diagonals AC is equal to 6 cm and BD is equal to 8 cm }. \]
\[\text{ Also, it is given that the diagonals bisect each other at right angle, at point O }. \]
\[ \therefore AO = OC = \frac{1}{2}AC = 3 cm\]
\[\text{ Also }, OB = OD = \frac{1}{2}BD = 4 cm\]
\[\text{ In right }\bigtriangleup AOB: \]
\[ {AB}^2 = {OA}^2 + {OB}^2 \]
\[ \Rightarrow {AB}^2 = (9 + 16) {cm}^2 \]
\[ \Rightarrow {AB}^2 = 25 {cm}^2 \]
\[ \Rightarrow AB = 5 cm\]
\[\text{ Thus, the length of each side of the quadrilateral is 5 cm } . \]
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