Question

Question 23
In quadrilateral ABCD, AB =7, BC=4, CD=11 and DA=3. If the length of the diagonal
BD is x, which of the following is true?
o
16<x
12<x<=14
14<x<=16
10<x<=12
07<x<=10
​

Answer 1

Given : In quadrilateral ABCD, AB =7, BC=4, CD=11 and DA=3.  

the length of the diagonal BD is x,

To Find : which of the following is true

16 < x

12< x < 14

14 < x  < 16

10 <  x  < 12

7 <  x  < 10

Solution:

AB = 7

BC = 4

CD = 11

DA = 3

in ΔABD

AB + AD >   BD   ( sum of two sides > third side)

=> 7 + 3  >  x

=> 10 > x

=> x < 10

in ΔBCD

BC + BD >   CD   ( sum of two sides > third side)

=> 4 + x  >  11

=>  x  > 7

From Both

7 < x < 10

x ∈ ( 7 , 10)

7 < x < 10  is true

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