Question

Is it possible to construct a quadrilateral abcd in which ab =1.5 cm, ad =3 cm, cd =2cm, ac =6.5cm, bd =5 cm? If not give reason?

Answer 1

Answer:

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Answer 2

$\huge\red{\underline{\overline{\mathbb{ANSWER:}}}}$

$\bf\underline{\underline{\red{GIVEN :}}}$

⠀⠀⠀⠀⠀$\red\bigstar \: AB = 1.5 \: cm.$

⠀⠀⠀⠀⠀⠀$\red\bigstar \: AD = 3 \: cm.$

⠀⠀⠀⠀⠀⠀⠀$\red\bigstar \: CD = 2 \: cm.$

⠀⠀⠀⠀⠀⠀⠀⠀$\red\bigstar \: AC = 6.5 \: cm.$

⠀⠀⠀⠀⠀⠀⠀⠀⠀$\red\bigstar \: BD = 5 \: cm.$

$\bf\underline{\underline{\red{TO \: FIND :}}}$

$\red\bigstar$ Is it possible to construct a Quadrilateral ABCD ?

$\bf\underline{\underline{\red{SOLUTION :}}}$

We know that in the triangle sum of any 2 sides is greater than third side,

$\Large\bf\red{In\:\triangle{ABD}\:\: :}$

$→ AB = 1.5 \: cm$

$→ AD = 3 \: cm$

$→ BD = 5 \: cm$

$→ AB + AD = BD$

$→ 1.5 + 3 = 5$

$→ 4.5<5$

$\Large\bf\red{In\:\triangle{ACD}\:\: :}$

$→ AC = 6.5 \: cm$

$→ CD = 2 \: cm$

$→ AD = 3 \: cm$

$→ CD + AD = AC$

$→ 2 + 3 = 6.5$

$→ 5<6.5$

$\red\bigstar$ These both triangles are impossible.

$\small\boxed{{\sf\red{Hence, \: it \: is \: not \: possible \: to \: construct \: a \: Quadrilateral \: ABCD.}}}$

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