Question : Two medians JX and KY of $\triangle \mathrm{JKL}$ intersect each other at Z at right angles. If KL = 22 cm and KY = 12 cm, then what is the length of JX?

Option 1: $6 \sqrt{19} \mathrm{~cm}$

Option 2: $3 \sqrt{57} \mathrm{~cm}$

Option 3: $2 \sqrt{57} \mathrm{~cm}$

Option 4: $4 \sqrt{19} \mathrm{~cm}$

Question : The three sides of a triangle are 7 cm, 9 cm, and 8 cm. What is the area of the triangle?

Option 1: $12 \sqrt{3} \;\mathrm{Sq} . \mathrm{cm}$

Option 2: $10\sqrt{3} \;\mathrm{Sq} . \mathrm{cm}$

Option 3: $12 \sqrt{5} \;\mathrm{Sq} . \mathrm{cm}$

Option 4: $2 \sqrt{5} \;\mathrm{Sq} . \mathrm{cm}$

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 : In an equilateral triangle, the circumradius is 14 cm. What is the length of the median in this triangle?

Option 1: $14 \sqrt{3} \mathrm{~cm}$

Option 2: $21 \mathrm{~cm}$

Option 3: $18 \sqrt{3} \mathrm{~cm}$

Option 4: $7 \sqrt{3} \mathrm{~cm}$

Question : In an equilateral triangle STU, inradius is $5 \sqrt{3 }\mathrm{~cm}$. What is the length of the side of this equilateral triangle?

Option 1: $20 \sqrt{3} \mathrm{~cm}$

Option 2: $18 \sqrt{3} \mathrm{~cm}$

Option 3: $30 \mathrm{~cm}$

Option 4: $24 \mathrm{~cm}$