In a quadrilateral ABCD - AB -7 cm - BC -5 cm - AC -9 cm - AD -6 cm - CD -2 cm- Which of the following options is true about the construction of aquadrilateral ABCD-A- None of theseB- It is possible to draw the quadrilateralC- It is not possible to draw the quadrilateral since AD - DC - ACD- It is possible to draw the quadrilateral since AD - DC - AC

The correct option is C It is not possible to draw the quadrilateral since AD + DC lt; ACIn a triangle, sum of any two sides should be greater than the thir ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Construction of a Quadrilateral When Three Sides and Two Diagonals Are Given.

In a quadrila...

Question

In a quadrilateral ABCD, AB = 7 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm. Which of the following options is true about the construction of a quadrilateral ABCD?

It is possible to draw the quadrilateral

No worries! We‘ve got your back. Try BYJU‘S free classes today!

It is not possible to draw the quadrilateral since AD + DC < AC

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

It is possible to draw the quadrilateral since AD + DC < AC

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B It is not possible to draw the quadrilateral since AD + DC < AC
In a triangle, sum of any two sides should be greater than the third side. A quadrilateral is made up of two triangles.

It is given that AD = 6 cm, CD =2 cm and AC = 9 cm. AC $>$ AD + CD. This does not satisfy triangle inequality and hence the quadrilateral ABCD cannot be drawn.

Suggest Corrections

Similar questions

If you are given AB = 5 cm, BC = 6 cm, CD = 7 cm, DA = 6 cm and $∠ A B C$ = $60^{\circ}$ , is it possible to draw the quadrilateral ABCD?

Construct, if possible a quadrilateral ABCD in which AB=6 cm, BC =7 cm, CD =3 cm, AD =5.5 cm and AC =11cm, Give reasons for not being able to construct, if you cannot.

Construction of a unique quadrilateral ABCD is possible with AB = 4cm, BC = 6cm, AC = 7cm, CD = 5cm and BD = 8cm.

Is it possible to construct a unique quadrilateral ABCD with AB = 5cm, BC = 6cm, CD= 7cm, $∠ A B C =$ $40^{\circ}$ and $∠ B C D =$ $55^{\circ}$ ?

Q. Construct, if possible, a quadrilateral ABCD in which AB = 6 cm, BC = 7 cm, CD = 3 cm, AD = 5.5 cm and AC = 11 cm. Give reasons for not being able to construct, if you cannot. (Not possible, because in triangle ACD, AD + CD < AC).

Join BYJU'S Learning Program