Question : The lengths of two parallel sides of a trapezium are 15 cm and 20 cm. If its area is 175 cm², then its height is:

Option 1: 15 cm

Option 2: 10 cm

Option 3: 20 cm

Option 4: 25 cm

Question : Two medians DM and EN of $\triangle$DEF intersect each other at O at right angles. If EF = 20 cm and EN = 12 cm, then what is the length of DM?

Option 1: 20 cm

Option 2: 12 cm

Option 3: 18 cm

Option 4: 15 cm

Question : 360 cm² and 250 cm² are the areas of the two similar triangles. If the length of one of the sides of the first triangle is 8 cm, then the length of the corresponding side of the second triangle is:

Option 1: $6\frac{1}{5}\;\operatorname{ cm}$

Option 2: $6\frac{1}{3}\;\operatorname{ cm}$

Option 3: $6\frac{2}{3}\;\operatorname{ cm}$

Option 4: $6\;\operatorname{ cm}$

Question : Let $ABC$ and $PQR$ be two congruent right-angled triangles such that $\angle A=\angle P=90^{\circ}$. If $BC=13\ \text{cm}$ and $PR=12\ \text{cm}$, then find the length of $AB$.

Option 1: 25 cm

Option 2: 20 cm

Option 3: 10 cm

Option 4: 5 cm

Question : X, Y, and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?

Option 1: 10 cm

Option 2: 10.5 cm

Option 3: 9.5 cm

Option 4: 9 cm