A triangle has integer length sides. If two sides of the triangle are 18 and \(44\), how many possible lengths are there for the third side?
A triangle has integer length sides. If two sides of the triangle are 18 and \(44\), and the triangle is obtuse, how many possible lengths are there for the third side?
+130077 A triangle has integer length sides. If two sides of the triangle are 18 and 44 , how many possible lengths are there for the third side?
18 + x > 44 18 + 44 > x
x > 44 - 18 62 > x
x > 26
So
26 < x < 62 ......number of possible integer lengths = 61 - 27 + 1 = 35
+130077 A triangle has integer length sides. If two sides of the triangle are 18 and 44 , and the triangle is obtuse, how many possible lengths are there for the third side?
If obtuse
18^2 + x^2 < 44^2 44^2 + 18^2 < x^2
x^2 < 44^2 -18^2 2260 < x^2
x^2 < 1612 ceiling sqrt (2260) < x = 48
x < floor sqrt (1612) = 40
So 48 - 40 + 1 = 9 possible integer lengths
