Final answer:
The length of QS can be any value greater than or equal to 0. triangle inequality, in Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
Step-by-step explanation:
To find the length of QS, we can use the triangle inequality theorem. According to the theorem, 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 have RS = 19 and QR = 32. Therefore, we can write the inequality equation as QR + QS > RS.
Substituting the given values, we have 32 + QS > 19. Solving for QS, we get QS > 19 - 32, which simplifies to QS > -13. However, length cannot be negative, so the minimum value for QS is 0.
Therefore, the length of QS can be any value greater than or equal to 0. None of the given options (a) 13, (b) 51, (c) 17, (d) 15, are correct.
According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side. A polygon bounded by three line-segments is known as the Triangle. It is the smallest possible polygon.