A median is a line segment drawn from the vertex of a triangle to the

midpoint of the opposite side.

A triangle has an area of 72 cm2

. The length of one side is 12 cm and the

length of the median to this side is 13 cm.

Determine the length of the other two sides of the triangle.

# Mathematics Olympiad Resource

high school,elementary school, algebra, geometry, numbers and many other mathematics olympiad problems and competitions

## 11/27/2011

## 7/18/2011

### The Case of Confused Cashier

Taken from South East Asian Mathematics Competition (SEAMC) 2010 in Bangkok, Thailand.

Mr. Smith went into his local bank with a cheque for an amount in Dollars and Cents. He asked the cashier to give him cash for the amount on the cheque. However, she confused the Dollars and cents. So Mr. Smith received Dollars for the amount of cents on the cheque, and cents for the amount of Dollars (e.g if the cheque was for $22.43, Mr. Smith would have been given $43.22)

Mr. Smith left the bank and bought a newspaper for 50 cents. After this, Mr. Smith realised he had exactly three times as much money left as the value of the original cheque.

How much was the original cheque for?

For another SEAMC past problems visit the official site.

Mr. Smith went into his local bank with a cheque for an amount in Dollars and Cents. He asked the cashier to give him cash for the amount on the cheque. However, she confused the Dollars and cents. So Mr. Smith received Dollars for the amount of cents on the cheque, and cents for the amount of Dollars (e.g if the cheque was for $22.43, Mr. Smith would have been given $43.22)

Mr. Smith left the bank and bought a newspaper for 50 cents. After this, Mr. Smith realised he had exactly three times as much money left as the value of the original cheque.

How much was the original cheque for?

For another SEAMC past problems visit the official site.

## 6/04/2011

### Harvard–MIT Mathematics Tournament (Problem and Solution)

This high school mathematics tournament is sponsored by Harvard and MIT. HMMT is one of the largest math contests in the United States (based on opinion in the official site).

Well, The 2011 Harvard-MIT Mathematics Tournament was held on Saturday, February 12, 2011. All the archives (including problems and solutions) can be download here:

Well, The 2011 Harvard-MIT Mathematics Tournament was held on Saturday, February 12, 2011. All the archives (including problems and solutions) can be download here:

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