Question

The diagonal 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

We know in rhombus diagonals bisect each other at right angle.

In ΔAOB

BO = \(\frac{BD}{2}\) = \(\frac{6}{2}\) = 3 cm

AO = \(\frac{AC}{2}\) = \(\frac{8}{2}\) = 4 cm

Using pythagorous theorem in ΔAOB

AB² = AO² + BO²

AB² = 4² + 3²

AB² = 16 + 9

AB² = 25

AB = \(\sqrt{25}\) = 5 cm

Therefore length of each side of a rhombus ABCD is 5 cm.