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What is the perimeter? If necessary, round to the nearest tenth.
a=24
b=45
c=?

User Watson
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1 Answer

3 votes

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.

User Drg
by
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