Question

ABCD is a rhombus whose diagonals intersect at O.
If AB = 10 cm, diagonal BD = 16 cm, find the length
of diagonal AC.​

Answer 1

Answer:

12cm.

Step-by-step explanation:

given: AB is 10cm and BD is 16

so, OB= OD= 16/2

that is equal to ob= od= 8cm

then, we use the formula hypotenuse.

AB square _ OB square= OC square.

10× 10-. 8×8= OC square

100 - 64= OC square

36= OC square

so, OC= √36= 6cm.

then, the length of diagonal AC= 6×2= 12 cm.

Answer 2

Answer:

Given:- ABCD is a rhombus ,

whose one side AB is 10 cm

and diagonal BD is 16cm

To Find:-

The length of the diagonal AC

Solution:-

As we know that,

• Diagonals of a rhombus perpendicularly bisect each other .
• All sides of a Rhombus are equal in length .

Now, Diagonals BD and AC bisect at a point o

so

as BD = 16cm (given)

now,

DO =OB = 8 Cm

And all the length of the rhombus are equal

that means ,

AB = BC = CD = AD = 10cm

Now, In ΔBOC,

OC Is the height of the Δ

OB is the base of the Δ

BC is the Hypotenuse of the Δ

By applying pythagoras Theorem,

OB = 8cm

BC = 10cm

OC = ?

BC² = OC² + OB²

(10)² = OC² + ( 8)²

OC² + (8)² = ( 10)²

OC² = (10)² - (8)²

OC² = 100 -64

OC² = 36

OC = √36

OC = 6

Therefore OC = 6cm

Now ,

AC = 2×OC ( As diagonals bisect each other )

AC = (2 × 6 )cm

AC = 12Cm

Therefore, The length of the diagonal AC is 12cm

Heres, also the diagram of the rhombus in above attachment in order to understand it .