Question

ABCD is a rhombus such that OA = 12cm, CB = 13cm and OB = 5cm. Find the values of x, y and z.

Answer 1

Answer:

so rhombus is a parallelogram

so OA = OC = 12 cm

similarly OB = OD = 5 cm

Answer 2

In triangle OBC :-

${13}^{2} = {5}^{2} + {y}^{2}$

( Diagonals of rhombus bisect at 90°. Hence we can use pyrhagoras theorem)

$169 = 25 + {y}^{2}$

$y = 12cm$

From, here we conclude that diagonal bisect each other equally.

Hence, Z = 5 cm

Now,

In triangle OAB :-

We again use pyrhagoras theorem -

${x}^{2} = {5}^{2} + {12}^{2}$

$x = 13cm$