The smallest integer x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle is 11
Using the triangular theorem which states that the sum of any two sides of a triangle must be less than the third side.
Given the side length of the triangle to be a, b and c
a = x
b = x+5
c = 2x - 15
According to the theorem;
b < a+c
x+5 < x + 2x - 15
x + 5 < 3x - 15
Collect the like terms
x - 3x < -15 - 5
-2x < -20
x > -20/-2
x > 10
Since x is greater than 10, let x be 11
Hence the smallest integer x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle is 11
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