Area = 24 cm² and base = 4.8 cm.

We know that,

⇒ Area of rectangle = Base × Height

⇒ 24 = 4.8 × Height

⇒ Height = $\dfrac{24}{4.8}$ = 5 cm.

Steps of construction :

1. Let adjacent sides AB = 4.8 cm and BC = 5 cm.

2. Draw a line segment AB = 4.8 cm.

3. Draw AX ⊥ AB and BY ⊥ AB.

4. With A as center and radius equal to 5 cm draw arc cutting AX at D.

5. With B as center and radius equal to 5 cm draw arc cutting BY at C.

6. Join CD.

Hence, ABCD is the required rectangle.