Can the sides of a triangle have lengths 1, 2, and 10?

Mathematics

1 answer:

serious [3.7K]3 years ago

3 0

Answer:

Step-by-step explanation:

According to the triangle inequality theorem, for it to be a triangle the sum of two sides must be greater than the third side, but it isn't so for

1 + 2 is less than 10

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The junior senator can do a labyrinth in 50 minutes. The senior senator can do a labyrinth in 30 minutes. Working together, how

vladimir2022 [97]

Answer:

$225\:\text{minutes}$

Step-by-step explanation:

To navigate through this problem, start by finding how much each senator can complete in a fixed amount of time. I'll choose 10 as it's the greatest common factor of 30 and 50.

In 10 minutes, the junior senator can complete $\frac{10}{50}=\frac{1}{5}$ of the labyrinth.

In 10 minutes, the senior senator can complete $\frac{10}{30}=\frac{1}{3}$ of the labyrinth.

Therefore, working together, they can complete $\frac{1}{5}+\frac{1}{3}=\frac{8}{15}$ of the labyrinth in 10 minutes. Thus, it will take them $\frac{15}{8}\cdot 10 \text{ minutes}=18.75\:\text{minutes}$ to complete one labyrinth.