ABC is triangle in which AB = 3 cm, BC= 5 cm and AC = 4 cm. AD is a perpendicular from A to BC. Find the length of AD.

The ratio of the ages of a man and his wife is 4 : 3. After 4 years, the ratio will be 9:7. If at the time of marriage the ratio was 5: 3, then how many years ago were they married?

$if x+y=a, x^2+y^2 and x^3+y^3=c^3 then show that a^3+2c^3=3a{b}^2$

Solve the following Problem: 

The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another number aged 39 years. What will be the average age of the present committee?

The ratio of the salary of A, B & C is 7: 5: 3. If B gets Tk. 222 more than what C gets, then what is the salary of A?