Find x if the sides of a triangle were 24 and 10
What are the different solutions
the 3rd side of a triangle must be long enough to connect the ends of the other two sides
... it must also be short enough that the other two sides can connect its ends
difference of other two sides <
... 3rd side < sum of other two sides
x+24>10 AND x+10>24 AND 24+10> x
x > -14 AND x > 14 AND x < 34
so 14 < x < 34
To find x, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the sides of the triangle are 24 and 10, we can let x represent the third side. So now we have the following inequalities:
10 + x > 24 (to satisfy the inequality with the side of length 24)
24 + x > 10 (to satisfy the inequality with the side of length 10)
Let's solve these inequalities one by one:
10 + x > 24:
Subtracting 10 from both sides, we get:
x > 14
24 + x > 10:
Subtracting 24 from both sides, we get:
x > -14
Combining the results, we have:
-14 < x < 14
So, the possible values for x would be any number between -14 and 14, excluding the endpoints. In other words, x can be any real number between -14 and 14, excluding -14 and 14 themselves.