Question

select all of the sets of side lengths that will form a triangle. 7, 6, 11 9, 5, 13 8, 3, 11 5, 5, 9 7, 7, 15 two of a triangles side lengths are 10 cm and 18 cm. what is the largest possible whole number length of the third side? 1 point your answer

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check the sets of side - lengths

For 7, 6, 11:

$7 + 6=13>11$, $7 + 11 = 18>6$, $6+11 = 17>7$. So it can form a triangle.

For 9, 5, 13:

$9 + 5=14>13$, $9 + 13 = 22>5$, $5 + 13 = 18>9$. So it can form a triangle.

For 8, 3, 11:

$8 + 3=11$, which does not satisfy the triangle - inequality theorem ($a + b>c$ for all sides $a$, $b$, $c$ of a triangle). So it cannot form a triangle.

For 5, 5, 9:

$5 + 5=10>9$, $5 + 9 = 14>5$, $5+9 = 14>5$. So it can form a triangle.

For 7, 7, 15:

$7 + 7=14<15$, which does not satisfy the triangle - inequality theorem. So it cannot form a triangle.

Step3: Find the largest possible whole - number length of the third side given two sides of lengths 10 cm and 18 cm

Let the lengths of the two given sides be $a = 10$ and $b = 18$. According to the triangle - inequality theorem, $|a - b|$|10 - 18|=8$ and $10 + 18 = 28$. So $8

Answer:

The sets of side - lengths that form a triangle are 7, 6, 11; 9, 5, 13; 5, 5, 9. The largest possible whole - number length of the third side is 27.