Final answer:
No, it is not possible to draw a triangle with sides of lengths 10, 5, and 4, because they do not satisfy the triangle inequality theorem, which requires the sum of the lengths of any two sides to be greater than the length of the third side.
Step-by-step explanation:
To determine if it's possible to draw a triangle with sides of lengths 10, 5, and 4, we can use the triangle inequality theorem. This 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 this case, we add the smaller two sides (5 + 4 = 9) and compare this sum to the length of the longest side, which is 10.
Since 9 is not greater than 10, the sum of the lengths of the two smaller sides does is not greater than the length of the longest side. Therefore, according to the triangle inequality theorem, a triangle with sides of lengths 10, 5, and 4 cannot be constructed, because it does not satisfy the necessary condition for the sides of a triangle.
Consider a scenario where you are asked to make a scale drawing of a triangular object. If a side of the actual object is 5.5 meters and the scale factor is 1/20, the length of that side in the scale drawing would be 5.5 meters multiplied by 1/20, resulting in 0.275 meters, or 27.5 centimeters. This calculation shows how scale factors are used to create smaller, proportional representations of objects.