Question

Two sides of a triangle measure 27 inches and 32 inches. Which could represent the length of the third side?

Answer 1

The third side is greater than 5 but less than 59.

Explanation:

Remember: Given any two sides of a triangle, the length of the third side is greater than the difference but less than the sum of the length of the two given sides.

So 27 and 32 The given two sides

32 - 27 = 5 Greater than the difference (greater than 5)

32 + 27 = 59 Less than the sum (less than 59)

Answer 2

Explanation:

The third side could have dimension x

32 - 27 < x < 32 + 27

5 < x < 59

There are a few special triangles

Equilateral triangle could have legs

27, 32, 27

or

32, 27, 32

A right triangle could have the third side

√(27² + 32²) = √1753 which is about 41.87

or

√(32² - 27²) = √295 which is about 17.18

Notice all these fit within the original limits specified.