PROBLEM # 1
What is the sum of angles inside the shape formed by connecting points C, A, B, D, back to C?

PROBLEM #2
What is the The equation of a line perpendicular to 2x+y-4=0 that passes through the origin?

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Problems from 04/14/11

PROBLEM # 1
x is an integer. x > 4 and  - x < - 1. What are the possible values of x?

SOLUTION 1
x = 5, 6 ,....

PROBLEM #2
The triangle 5,12,13 has an area A=30 and a perimeter P=30, so A/P is 1. The triangle 9,75,78 has an area A=324 and a perimeter P=162, so A/P is 2. Find a triangle whose A/P is 10.

SOLUTION 2
Any arbitrary triangle a, b, c: scale it to (a, b, c)*10*P*4/SQRT[P*(P-2a)*(P-2b)*(P-2c)], where P=a=b+c.
(Solution provided by Ranganath Nayak)

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