The base of a triangle is 11. The other two sides are integers and one of the sides is twice as long as the other. What is the shortest possible length of a side of the triangle?
The shortest possible length is 4.
Shortest side = X.
Other side = 2X.
x + 2x > 11
3x > 11
X > 11/3
X > 3 2/3
X = 4 = Shortest possible length.
2X > 22/3
2X > 7 1/3
2X = 8.
How long does it take the snail to travel 2 inches
To find the shortest possible length of a side of the triangle, we need to consider the properties of triangles.
Let's denote the shortest side length as x.
Given that the base of the triangle is 11, the other two sides are integers, and one side is twice as long as the other, we can set up an equation based on the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.
In this case, we have:
11 + x > 2x (since one side is twice as long as the other)
11 > x (subtracting x from both sides of the inequality)
To determine the shortest possible length of a side, we should find the largest integer that satisfies this inequality.
Since x is an integer, the largest possible integer that is less than 11 is 10.
Therefore, the shortest possible length of a side of the triangle is 10.