Question

1 multiple choice 4 points
jennie’s math tutor drew three lines to create a right angle scalene triangle in her
math notebook.
which of the following are the possible whole number lengths of the three segments?
33,35,48
7,24,25
2,3,4
16,17,23

2 multiple choice 4 points
eva has four sets of straws. the measurements of the straws are given below. which
set of straws could not be used to form a triangle?
set 2: 2 cm, 3 cm, 8 cm
set 1: 4 cm, 4 cm, 7 cm
set 4: 5 cm, 12 cm, 13 cm
set 3: 3 cm, 4 cm, 5 cm

3 multiple choice 4 points
the lengths of three sides of a triangle are 5, 9, and x, all measured in centimeters.
what are all possible values of x?
4 < x < 14
0 < x < 14
3 < x < 9
5 < x < 15

Explanation:

Question 1

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\) (where \(c\) is the hypotenuse, the longest side). Also, a scalene triangle has all sides of different lengths.

Step2: Check each option

• Option [33,35,48]: \(33^2 + 35^2 = 1089 + 1225 = 2314\), \(48^2 = 2304\). \(2314

eq2304\), not a right triangle.

• Option [7,24,25]: \(7^2 + 24^2 = 49 + 576 = 625\), \(25^2 = 625\). So \(7^2 + 24^2 = 25^2\), and all sides are different (scalene).
• Option [2,3,4]: \(2^2 + 3^2 = 4 + 9 = 13\), \(4^2 = 16\). \(13

eq16\), not a right triangle.

• Option [16,17,23]: \(16^2 + 17^2 = 256 + 289 = 545\), \(23^2 = 529\). \(545

eq529\), not a right triangle.

Step1: Recall triangle inequality theorem

For three lengths \(a\), \(b\), \(c\) (where \(c\) is the longest), \(a + b>c\) must hold.

Step2: Check each set

• Set 1: \(4 + 4 = 8>7\), \(4 + 7 = 11>4\), \(4 + 7 = 11>4\). Can form a triangle.
• Set 2: \(2 + 3 = 5<8\). Does not satisfy the triangle inequality.
• Set 3: \(3 + 4 = 7>5\), \(3 + 5 = 8>4\), \(4 + 5 = 9>3\). Can form a triangle.
• Set 4: \(5 + 12 = 17>13\), \(5 + 13 = 18>12\), \(12 + 13 = 25>5\). Can form a triangle.

Step1: Recall triangle inequality theorem

For a triangle with sides \(a\), \(b\), \(x\), \(|a - b|

Step2: Apply the theorem

Given \(a = 5\), \(b = 9\). Then \(|9 - 5|=4\) and \(9 + 5 = 14\). So \(4

Answer:

[7,24,25]

Question 2