Question

3 straws are shown. The length of one straw is 12 inches, the length of another straw is 9 inches, and the length of the last straw is unknown. Marlena has 3 straws. Two straws have the lengths shown. She does not know the length of the shortest straw, but when she forms a triangle with all three, the triangle is obtuse. Which are possible lengths of the shortest straw? Check all that apply. 5 inches 6 inches 7 inches 8 inches 9 inches.

Answer 1

Answer:

5 inches 6 inches and 7 inches

Step-by-step explanation:

5 inches gives an angle of 115 degrees.

6 inches gives an angle of 104 degrees.

7 inches gives an angle of 96 degrees

These three triangles are obtuse triangles

8 inches gives an angle of 89.6 degrees.

9 inches gives an angle of 83.6 degrees.

These two triangles are acute triangles.

Answer 2

The length of the shortest straw has been 5, 6 and 7 inches by prime factorization.

An obtuse triangle has been formed with all the three sides different measurement.

Sides of an obtuse triangle

The sides in the obtuse triangle has been given by:

$a^2\;+\;b^2\;=\;c^2$

Where, the side one, $a=12$

The side two of triangle. $b=9$

The third side of the triangle, c has bee n given by substituting the values as:

$12^2=c^2\;+\;9^2\\144\;-\;81=c^2\\\sqrt{144\;-\;81}=c\\7.93=c$

The length of the shortest straw has been 5, 6 and 7 inches by prime factorization.

For more information about obtuse triangle, refer to the link:

https://brainly.com/question/2617159