Question

EACH is a rhombus in fig. where OH=12 OE=x OA=y OC=5 EA=13 Find x,y,z​

Answer 1

In a rhombus, diagonals are perpendicular to each other and bisect each other.

∴BO=OD=12cm

∴y=12cm

and

CO=OA=5cm

∴x=5cm

Since BC²=CO²+BO², by substituting values we get:

BC2=(12)²+(5)²

⇒BC=169

⇒BC=13cm

Since all sides are equal, BC=CD

∴z=13cm

Hence, the value of x is 5cm and the value of z is 13cm.

Answer 2

Given: EACH is a rhombus

OH=12, OE = x, OA = y  OC = 5, EA = z

To Find:  x, y, z ?​

Solution:

EACH is a rhombus

Diagonals of a rhombus bisect each other perpendicularly

Hence

OH = OA

=> 12 = y

Hence y = 12

OC = OE

=> 5 = x

=> x =  5

EA² = OE² + OA²

=> z² = x²  + y²

=> z² = 5²  + 12²

=>   z = 13

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