Question

& ABCD is a parallelogram whose diagonals intersect each other at right angles. If
the length of the diagonals is 6 cm and 8 cm, find the lengths of all the sides of
the parallelogram.​

Answer 1

well,

according to the information that ABCD is a parallelogram and it's daigonals are un equal and they intersect each other at right angles.

we can tell that the parallelogram is an rhombus.

By applying Pythagoras theroum:-

$ab {}^{2} = 3 {}^{2} + 4 {}^{2}$

(~ab is the side and and at LHS it is the sum of the square of the half's of the daigonals as they bisect each other.)

$ab {}^{2} = 9 + 16 = 25$

$ab { }^{2} = 5 {}^{2}$

Therefore:

ab= 5cm

as all the sides of a rhombus are equal

so ab=bc=cd=ad=5cm.