Question

Sarah said, "There is only one possible third side for a right triangle with two sides measuring 9 units and 15 units.'

Answer 1

The answers: 3•sqrt34 and 12

Depending on the theorem of Pythagoras
Answer N1: sqrt(9^2 + 15^2)
Answer N2: sqrt(15^2 - 9^2)

Answer 2

The two possible answers for the third side of the right triangle are 6 and 24.

What is the triangle inequality theorem?

The Triangle Inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

So, a difference of two sides <x< sum of two sides, will give you the possible length of a triangle.

Sarah said, "There is only one possible third side for a right triangle with two sides measuring 9 units and 15 units.'

The two possible answers for the third side of the right triangle are;

$\rm 15-9 < x < 15+9\\\\6 < x < 24$

The possible length of the third side of a triangle.

For checking the possible length:

15 + 9 > 7 (a+b>c)

9 + 7 > 15 (b+c>a)

7+ 15 >9(a+c>b)

Which satisfy the triangle inequality theorem.

Hence, the two possible answers for the third side of the right triangle are 6 and 24.

Learn more about triangles here;

brainly.com/question/12930526

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