In a quadrilateral ABCD, AB=6 cm, BC=18 cm, CD=6 cm and DA=10 cm. If the diagonal BD=x, then which one of the following is correct?
- A. 8 \lt x \lt 12
- B. 12 \lt x \lt 16 ✓
- C. 16 \lt x \lt 18
- D. 18 \lt x \lt 20
Correct Answer: B. 12 \lt x \lt 16
Explanation
A diagonal splits a quadrilateral into two triangles, and in any triangle, the third side must be strictly between the difference and sum of the other two sides. For triangle ABD, 10-6 \lt x \lt 10+6, so 4 \lt x \lt 16. For triangle BCD, 18-6 \lt x \lt 18+6, so 12 \lt x \lt 24. The values of x satisfying both conditions lie in the intersection: 12 \lt x \lt 16.
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