Question

In rhombus ABCD, AC and BD intersect each other at O .If DO= 6 cm, CO= 8 cm, find AO and BO and AB in cm​

Answer 1

Answer:

In rhombus ABCD, diagonals AC and BD intersect each other at point O. If cosine of angle CAB is 0.6 and OB=8 cm, then the lengths of the side and the major & minor diagonals of the rhombus are respectively

A

12cm, 15cm, 22cm.

B

10cm, 16cm, 12cm.

C

30cm, 26cm, 32cm.

D

40cm, 36cm, 42cm.

MEDIUM

ANSWER

We know that diagonal of rhombus are perpendicular to each other.

So angle AOB is 90 degree

So triangle AOB is right-angled triangle.

Let angle CAb =a

cos a=0.6

Given OB=8cm

tan a=

OA

OB

- eq. 1

sin a =

AB

OB

- eq. 2

tan a=

cosa

sina

-eq. 3

sina=

1−cos

2

a

- eq. 4

By equation 4 we get

sina=0.8

By equation 3 we get

tan a=

3

4

using equation 1 we get length of OA=6

By equation 2 we get length of AB =10

So Lenght of sides are 10 cm , length of major diagonal is 8x2=16 , length of minor diagonal =6x2=12

So correct answer is Option B

Answered By

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