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?
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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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