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Question

Can we draw a quadrilateral ABCD with following measurements: AB = 3cm, BC = 5cm, AD = 4cm, CD = 7cm and BD = 8cm?


A

No, it is impossible

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B

With the measure of extra angle, Yes

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C

With the measure of other diagonal, Yes

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D

Yes, definitely

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Solution

The correct option is A

No, it is impossible


If we have the measures of all the sides of a quadrilateral and its one diagonal, we can draw two triangles and hence, form a quadrilateral.

ABCD comprises of two triangle ADB & CDB

In Δ ADB, AB = 3cm, BD = 8cm, and AD = 4cm

Since, AB + AD < BD

ADB can't be constructed.

So, quadrilateral ABCD can't be constructed.


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