In the adjoining figure, XY is parallel to BC. If XY divides the triangle into two equal parts, then $\dfrac{AX}{AB}$ equals:

1. $\dfrac{1}{\sqrt{2}}$

2. $\dfrac{1}{2}$

3. $\dfrac{\sqrt{2} + 1}{\sqrt{2}}$

4. $\dfrac{\sqrt{2} - 1}{\sqrt{2}}$

Which of the following is true in the given figure, where AD is the altitude to the hypotenuse of a right-angled ΔABC?

(I) ΔABD ∼ ΔCAD

(II) ΔADB ≅ ΔCDA

(III) ΔADB ∼ ΔCAB

1. I and II

2. II and III

3. I and III

4. I, II and III

The areas of two similar triangles are 12 cm² and 48 cm² respectively. If the height of the smaller one is 2.1 cm, then the corresponding height of the bigger one is:

1. 0.525 cm

2. 4.2 cm

3. 4.41 cm

4. 8.4 cm

The areas of two similar triangles are 81 cm² and 144 cm². If the largest side of the smaller triangle is 27 cm, then largest side of the larger triangle is:

1. 24 cm

2. 36 cm

3. 48 cm

4. none of these