Question

The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18 inches and a second side that is 3 inches less than twice the third side, what are the possible lengths for the second and third sides?

Answer 1

Answer: One side could be 18 and the other side will be 33.

Step-by-step explanation:

• Side #1 = 18
• Side #2 = 2x - 3
• Side #3 = x

One way of setting up the inequality is: Side #2 + Side #3 > Side #1

$2x-3+x>18\\3x-3>18\\3x>18+3\\3x>21\\x>7$

Another way of setting up the inequality is: Side #1 + Side #3 > Side #2

$18+x>2x-3\\18+3>2x-x\\x<21$

Final way of setting up the inequality is: Side #1 + Side #2 > Side #3

$18+2x-3>x\\15>x-2x\\15>-x\\x>-15$

Therefore, we have the range for our value of x, which is between 7 and 21. Any possible value between works. Negative measurements are rejected. One of the sides would equal the x-value, while the other side would equal the value of 2x-3.