Construction of Quadrilaterals, Ex-17A

Question

Construct a quadrilateral ABCD in which AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ∠ABC = ∠ACD = 90°

Can anyone please send me the answer for the following question?

Answer 1

We are given that for a quadrilateral ABCD such that AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ∠ABC = ∠ACD = 90°

Let us construct the angle ∠ABC = 90° of some unknown length as

Now let us point the vertex A on the ray BY such that AB = 4 cm then we get

Now, let us point the vertex C on the ray BX such that AC = 5 cm then we get

We are given with another angle that is ∠ACD = 90°

Now, let us construct a ray CZ such that ∠ACD = 90° using the protractor then we get

Now, let us point the vertex D on the ray CZ such that AD = 5.5 cm then we get

Now by removing the rays and drawing the quadrilateral ABCD we get

Therefore, we can say that the quadrilateral ABCD such that AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ∠ABC = ∠ACD = 90° has been constructed.