Answer:
Explanation:
The perimeter of a triangle is the sum of the lengths of its sides. Therefore, to find the perimeter of the triangle with sides a = 24, b = 45, and c = ?, we need to add up the lengths of the known sides:
Perimeter = a + b + c
Plugging in the values, we get:
Perimeter = 24 + 45 + c
Simplifying, we get:
Perimeter = 69 + c
We still need to find the length of the third side, c. However, we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words:
a + b > c
24 + 45 > c
69 > c
Therefore, we know that c must be less than 69.
On the other hand, we can also use the fact that the difference between the lengths of any two sides of a triangle must be less than the length of the third side. In other words:
|a - b| < c
|24 - 45| < c
21 < c
Therefore, we know that c must be greater than 21.
Putting these two inequalities together, we have:
21 < c < 69
So the perimeter is:
Perimeter = 69 + c
And we know that:
21 < c < 69
Therefore, we can say that the perimeter is somewhere between:
69 + 21 = 90
and
69 + 69 = 138
Rounding to the nearest tenth, we get:
Perimeter ≈ 90.0 - 138.0
Therefore, the perimeter is somewhere between 90.0 and 138.0, depending on the actual length of the third side, c.