Any three lengths that satisfy the triangle inequality theorem can form the sides of a triangle. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In order for three lengths to form a triangle, they must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider three lengths: a, b, and c.
To determine if they can form a triangle, we need to check the following conditions:
a + b > c
a + c > b
b + c > a
If all three conditions are true, then the lengths a, b, and c can form a triangle.
For example, let's consider the lengths 3, 4, and 5.
3 + 4 > 5 (True)
3 + 5 > 4 (True)
4 + 5 > 3 (True)
Since all three conditions are true, the lengths 3, 4, and 5 can form a triangle.
Therefore, any three lengths that satisfy the triangle inequality theorem can be the lengths of the sides of a triangle.
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Total Surface Area of the Triangular prism = 30 ft².
Here, we have,
The triangular prism is attached.
The triangular prism shown has 2 triangular faces and 3 lateral faces.
here, we have,
Base of the triangle =2 ft
Height of the Triangle =3 ft
Area of one Triangular Face is:
A = 1/2 * 2 * 3 = 3 ft²
The dimensions of the lateral rectangles are:
2 ft by 3 ft
3 ft by height 3 ft
3 ft by height 3 ft
Therefore, total surface area of the triangular prism
=2(Area of one Triangular Face)+Area of 3 rectangular faces
= 2 *3 + ( 2*3 + 3*3 + 3*3)
= 6 + 24
= 30 ft²
Total Surface Area of the Triangular prism = 30 ft².
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