Question

construct a quadrilateral ABCD in which AB= 4.5 cm, AC= 6, AD= 5.5 and angle b= angle d= 90°​

Answer 1

Answer:

In the quadrilateral, ABCD, AB = 4 cm, AC = 5 cm, AD = 5.5 cm, and <ABC = <ACD = 90 deg.

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 = [5^2–4^2]^0.5 = 3 cm.

Again ACD is a right angled triangle with AC = 5 cm and AD = 5.5 cm (hypotenuse) and <ACD = 90 deg.

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.