If the base of an isosceles triangle has a length of 10, what is the shortest possible integral value for the length of each of the congruent sides?
You know that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.
So, the other two sides must be at least 11. That means each of the two congruent sides must be at least 6.
Well, if we're talking about an isosceles triangle, then we know that two of the sides are congruent. So let's assume that those two sides have a length of S. The third side, which is the base, has a length of 10. Now, to find the shortest possible integral value for S, we need to consider the triangle inequality theorem. This states that the sum of any two sides of a triangle must be greater than the third side. Since the two congruent sides have a length of S, their sum would be 2S. So we have the inequality 2S > 10. To find the shortest possible integral value for S, we round up to the nearest integer, which is 6. Therefore, the shortest possible integral value for the length of each of the congruent sides of the isosceles triangle is 6.
To find the shortest possible integral value for the length of each congruent side of an isosceles triangle with a base length of 10, we need to consider the triangle inequality theorem.
According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In the case of an isosceles triangle, the two congruent sides are equal.
Let's assume the length of each congruent side is 'x'. So, the triangle inequality can be expressed as follows:
x + x > 10
Simplifying the inequality, we have:
2x > 10
Dividing both sides by 2, we get:
x > 5
The length of each congruent side must be greater than 5. Since we are looking for the shortest possible integral value, the next smallest integer greater than 5 is 6.
Therefore, the shortest possible integral value for the length of each congruent side of an isosceles triangle with a base length of 10 is 6.
To find the shortest possible integral value for the length of each of the congruent sides of an isosceles triangle, we need to consider the concept of the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In an isosceles triangle, the two congruent sides are of equal length, while the base has a different length. Let's denote the length of each of the congruent sides as "x". According to the triangle inequality theorem, we can write the following inequality:
2x > 10
Simplifying this inequality, we have:
x > 10/2
x > 5
Since we are looking for the shortest possible integral value for x, we can conclude that x must be greater than 5. Therefore, the smallest integral value for x is 6.