Question

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

Answer 1

Steps of construction:
Step 1: Draw $AB=4cm$
Step 2: $Make\angle B={90}^{\circ }$
Step 3: $$\begin{gathered} A{C}^2=A{B}^2+B{C}^2 \\ {5}^2=4^2+B{C}^2 \\ 25-16=B{C}^2 \\ BC=3cm \end{gathered}$$
With B as the centre, draw an arc equal to 3 cm.
Step 4: Make $\angle C={90}^{\circ }$
Step 5: With A as the centre and radius equal to $5.5cm$, draw an arc and name that point as D.
Then, $ABCD$ is the required quadrilateral.