HMMT 二月 2003 · GEN1 赛 · 第 2 题
HMMT February 2003 — GEN1 Round — Problem 2
题目详情
- OP EN is a square, and T is a point on side N O , such that triangle T OP has area 62 and triangle T EN has area 10. What is the length of a side of the square?
解析
- OP EN is a square, and T is a point on side N O , such that triangle T OP has area 62 and triangle T EN has area 10. What is the length of a side of the square? Solution: 12 62 = P O · OT / 2 and 10 = EN · T N/ 2 = P O · T N/ 2, so adding gives 72 = P O · ( OT + 2 T N ) / 2 = P O · ON/ 2 = P O / 2 ⇒ P O = 12.