Construct a quadrilateral $A B C D,$ when $A B = 3 c m, C D = 3 c m, D A = 7.5 c m, A C = 8 c m, B D = 4 c m .$

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Solution

Given: $B D = 4 c m, A B = 3 c m$ and $A D = 7.5 c m$
We know that the sum of any two sides of a triangle is greater than the third side.
But $B D + A B = 4 + 3 = 7 c m$
$∴ B D + A B < A D$
So, This quadrilateral is not possible, as the sum of two sides of a triangle is less than the third side.

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Similar questions

Try to draw quadrilateral ABCD of these specifications:

(i) AB = 7 cm, BC =5 cm, CD = 4 cm, ∠B = 60°, ∠C = 140°.

(ii) AB = 8 cm, BC = 6 cm, CD = 5.5 cm, DA = 3 cm, ∠B = 50°.

(iii) AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm.

Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 5.4 cm, DA = 5.9 cm and diagonal AC = 8 cm? If not, why?

A B C D

A B = 4 cm, B C = 3.1 cm, C D = 3 cm, A D = 4.2 cm

A C = 5 cm

B D

A B C D

A B = 3 c m

B C = 4 c m

C D = 4 c m

D A = 5 c m

A C = 5 c m

Question 2
Find the area of a quadrilateral ABCD in which AB=3cm,BC=4cm,CD=4cm, DA = 5cm and AC= 5cm.

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