The sides of a quadrilateral ABCD in order are AB = 6, BC = 18, CD = 6, DA = 10. If the restriction is that the diagonal BD must be an integer, the number of such quadrilaterals is

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Solution

The correct option is C
3

1.In ∆ ABD, BD < 10 + 6 = 16.
In∆ BDC, BD + 6 > 18. (i.e.,) BD > 12. ∴ 12 < BD < 16.
∴ BD = 13, 14, 15 / 3 values only.

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Similar questions

The sides of a quadrilateral ABCD in order are AB = 6, BC = 18, CD = 6, DA = 10. If the restriction is that the diagonal BD must be an integer, the number of such quadrilaterals is

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In the adjoining figure, ABCD is a quadrilateral and AC is one of its diagonals. Prove that

(i) AB + BC + CD + DA > 2AC

(ii) AB + BC + CD > DA

(iii) AB + BC + CD + DA > AC + BD.

Let ABCD be a quadrilateral with diagonals AC and BD. Prove the following statements (Compare these with the previous problem);

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(b) AB + BC + CD + DA > 2AC;

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The sides of a quadrilateral ABCD in order are AB = 6, BC = 18, CD = 6, DA = 10. If the restriction is that the diagonal BD must be an integer, the number of such quadrilaterals is

The correct option is C 3 1.In ∆ ABD, BD < 10 + 6 = 16. In∆ BDC, BD + 6 > 18. (i.e.,) BD > 12. ∴ 12 < BD < 16. ∴ BD = 13, 14, 15 / 3 values only.

The correct option is C
3

1.In ∆ ABD, BD < 10 + 6 = 16.
In∆ BDC, BD + 6 > 18. (i.e.,) BD > 12. ∴ 12 < BD < 16.
∴ BD = 13, 14, 15 / 3 values only.