Question

Is it possible to construct a quadrilateral ABCD in which AB=1.5CM , AD=3CM , CD=2CM , AC=6.5CM , BD= 5CM? IF not give reason.


please solve this question its urgent​

Answer 1

Given : AB = 1.5 cm

AD = 3 cm

CD = 2 cm

AC = 6.5 cm

BD = 5 cm

To Find : Is it possible to construct a quadrilateral

Solution:

ABD and ACD are triangles in Quadrilateral

In a triangle Sum of any two sides is greater than third side

ΔABD

AB = 1.5  cm

AD = 3 cm

BD = 5 cm

1.5 + 3 = 4.5 < 5

Hence AB +  AD < BD

so this triangle is not possible

Similarly

ΔACD

AC = 6.5 cm

CD = 2 cm

AD = 3 cm

2 + 3 = 5 < 6.5

Hence CD + AD < AC

so  this triangle is also not possible

Hence not possible to construct   quadrilateral ABCD

Learn More:

can you construct the quadrilateral PLAN if PL=6cm,LA=9.5cm ...

https://brainly.in/question/20157232

Construct quadrilateral PQRS such that PQ=PS=PR= 9cm ,QR ..

brainly.in/question/13885649

Construct a quadrilateral MORE in which ME =4.5cm and OR=3.5cm ...

brainly.in/question/6231110

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.

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

Hope it Helps Buddy ♥️