Question

is it possible to construct a quadrilateral ABCD in which AB = 4cm, DA = 5.5cm, AC = 5cm and /_ B = /_ C = 90° ? if not , give reason




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Answer 1

Explanation:

Given measures are 

AS=3cm,BC=4cm,CD=5.4cm,DA=59cm and AC=8cm 

Here, consider the triangle ABC within the quadrilateral.

AB+BC=3+4=7cm and AC =8cm 

i.e., the sum of two sides of a triangle is less than the third side, which is absurd. 

Hence, we cannot construct such a quadrilateral. 

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Answer 2

Answer:

In the quadrilateral, ABCD, AB = 4 cm, AC = 5 cm, AD = 5.5 cm, and angle ABC = angle ACD = 90⁰

You can see that ABC is the basic Pythagoras right angled triangle in which AC = 5 cm (hypotenuse) AB = 4 cm, <ABC = 90 deg, hence BC = [5²– 4²]^0.5 = 3 cm.

Again ACD is a right angled triangle with AC = 5 cm and AD = 5.5 cm (hypotenuse) and angle ACD = 90 ⁰

Now for the construction of ABCD,

Draw a line AC = 5 cm. With A as center and a radius of 4 cm draw an arc. With C as as center and a radius of 3 cm draw another arc to cut the previous arc at B. Join A to B and C to B.

At C make an angle ACM of 90 deg. Let CM be 6 cm. With A as center and a radius of 5.5 cm, draw an arc to cut CM at D. Join AD.

You have the desired quadrilateral, ABCD.

Explanation:

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