three line segments have measures of 4 units, 6 units, and 8 units. Will the segments form a triangle?

Mathematics

1 answer:

Oliga [24]3 years ago

4 0

Given:

Three line segments have measures of 4 units, 6 units, and 8 units.

To find:

Will the segments form a triangle?

Solution:

We know that three line segments can form a triangle if the sum of two smaller sides is greater than the largest side.

Three line segments have measures of 4 units, 6 units, and 8 units. Here, the measure of the largest sides is 8 units.

The sum of two smaller sides is

$4+6=10$

$4+6>8$

Since the sum of two smaller sides is greater than the largest side, therefore the segments will form a triangle.

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There are 8 tennis players in a round robin tournament, which means each team will play every other team once. How many matches

Aliun [14]

<h3>Answer: 28</h3>

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Explanation:

Method 1

Imagine a table with 8 rows and 8 columns to represent all possible match-ups. You can actually draw out this table or just think of it as a thought experiment.

There are 8*8 = 64 entries in the table. Along the northwest diagonal, we have each team pair up with itself. This is of course silly and impossible. We cross off this entire diagonal so we drop to 64-8 = 56 entries.

Then notice that the lower left corner is a mirror copy of the upper right corner. A match-up like AB is the same as BA. So we must divide by 2 to get 56/2 = 28 different matches.

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Method 2

There are 8 selections for the first slot, and 8-1 = 7 selections for the second slot. We have 8*7 = 56 permutations and 56/2 = 28 combinations.

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Method 3

Use the nCr combination formula with n = 8 and r = 2

$n C r = \frac{n!}{r!(n-r)!}\\\\8 C 2 = \frac{8!}{2!*(8-2)!}\\\\8 C 2 = \frac{8!}{2!*6!}\\\\8 C 2 = \frac{8*7*6!}{2!*6!}\\\\ 8 C 2 = \frac{8*7}{2!}\\\\ 8 C 2 = \frac{8*7}{2*1}\\\\ 8 C 2 = \frac{56}{2}\\\\ 8 C 2 = 28\\\\$