Question

An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

2 < s < 18
6 < s < 12.8
s < 2 or s > 18
s < 6 or s > 12.8

Answer 1

is 2nd option aka B) 6 < s < 12.8

Explanation:

just took the "pre test"

Answer 2

Either the new side or 10 has to be the hypotenuse of a triangle.

Case one
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The hypotenuse is 10
10^2 = 8^2 + b^2
b^2 = 36
b = 6 so the new side has to be more than 6 but less than 10.

Case two
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The new side is the hypotenuse of a right triangle
8^2 + 10^2 = 64 + 100 = 164
sqrt(164) = 12.8
So the new side has to be less than 12.8 but greater than 6

Answer
The second one <<<< ===========
6 < s < 12.8