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Quadrilateral with sides 6, 18, 6 and 9 or 10: find diagonal BD from the triangle inequality

This type of question, asked 2 times: CDS 1 2024, CDS 2 2025. All 2 questions below, oldest first.

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  1. Question 1

    CDS 1 2024

    48
    In a quadrilateral ABCD, AB = 6 cm, BC = 18 cm, CD = 6 cm and DA = 10 cm. If diagonal BD = x, then which one of the following is correct ?

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  2. Question 2

    CDS 2 2025

    88
    A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : In a quadrilateral ABCD, AB=6AB = 6 units, BC=18BC = 18 units, CD=6CD = 6 units, DA=9DA = 9 units. What is the length of diagonal BD? Statement-I : The length of BD is an integer greater than 13. Statement-II : The length of BD is an even integer. Which one of the following is correct in respect of the above Question and the Statements?

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