Question

A) If a triangle has sides of 37 m and 52 m, what is a possible length for the third side? (1 point)
70 m
89 m
15 m
104 m

Answer 1

To find a possible length for the third side of a triangle given two sides, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let the two sides be \(a = 37 \, m\) and \(b = 52 \, m\), and let the length of the third side be \(c\).

The triangle inequalities we need to satisfy are:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Substituting the known values into the inequalities:

1. \(37 + 52 > c \implies 89 > c \implies c < 89\)
2. \(37 + c > 52 \implies c > 15\)
3. \(52 + c > 37\) (this is always true as long as \(c > -15\), which it will be).

So, we have:

- \(15 < c < 89\)

Now, let's evaluate the provided options:

1. 70 m (within the range)
2. 89 m (not valid; \(c\) must be less than 89)
3. 15 m (not valid; \(c\) must be greater than 15)
4. 104 m (not valid; exceeds the range)

Thus, the only possible length for the third side is **70 m**.