Question

The diagonals of a quadrilateral are of lengths are 6cm and 8cm. If the diagonals bisect each other at right angles, is it a rhombus or a square? Give reason:

Answer 1

Correct Question:-

The diagonals of a quadrilateral are of lengths are 6cm and 8cm. If the diagonals bisect each other at right angles, is it a rhombus or a square? Give reason:

Solution :

Let the ABCD be the quadrilateral

According to the question

AO = OC and OB =OD 

Now , By Applying Pythagoras Theorem

$ad {}^{2} = 4 {}^{2} + 3 {}^{2} \\ ad = 5 cm.$

$dc {}^{2} = 3 {}^{2} + 4 {}^{2} \\ dc = 5cm$

Similarly ,

BC = AB = 5cm

So AB = BC = DC = AD = 5cm .

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