10. m∠A = 8x – 2, m∠B = 2x – 8, and m∠C = 94 – 4x. List the sides of △ABC in order from shortest to longest.
Ac, AB, BC
AC, BC, AB
AB, AC, BC
BC, AC, AB
11. Which three lengths could be the lengths of the sides of a triangle?
6 cm, 23 cm, 11 cm
10 cm, 15 cm, 24 cm
22 cm, 6 cm, 6 cm
15 cm, 9 cm, 24 cm
12. Two sides of a triangle have lengths 6 and 13. Which expression describes the length of the third side?
at least 7 and less than 19
at least 7 and at most 19
greater than 7 and less than 19
greater than 7 and at most 19
Ac, AB, BC
AC, BC, AB
AB, AC, BC
BC, AC, AB
11. Which three lengths could be the lengths of the sides of a triangle?
6 cm, 23 cm, 11 cm
10 cm, 15 cm, 24 cm
22 cm, 6 cm, 6 cm
15 cm, 9 cm, 24 cm
12. Two sides of a triangle have lengths 6 and 13. Which expression describes the length of the third side?
at least 7 and less than 19
at least 7 and at most 19
greater than 7 and less than 19
greater than 7 and at most 19
-
10. The size of the angle gives the length of the opposite side. A narrow angle means a small side, while a large angle means a long side.
The three angles have to add up to 180°, so
(8x - 2) + (2x - 8) + (94 - 4x) = 180
6x + 84 = 180
6x = 96
x = 16
If x=16, ∠A=126°, ∠B = 24°, ∠C = 30°
So the shortest side is opposite ∠B, followed by opposite ∠C, followed by opposite ∠A
So: AC, AB, BC
11. For a triangle to "work", two sides cannot add up to less than the third side.
Think of a "triangle" that looked like this:
/-------------------\
where the left and right sides were of length 1, and the base was length 20. It can't be a triangle!
So, only the second one can be a triangle (the last one is actually a straight line!)
12. From this it follows that "At least 7" is not good enough - seven would again give a straight line.
And "at most 19" is not good enough - nineteen would again give a straight line.
So you want "Greater than 7 and less than 19"
The three angles have to add up to 180°, so
(8x - 2) + (2x - 8) + (94 - 4x) = 180
6x + 84 = 180
6x = 96
x = 16
If x=16, ∠A=126°, ∠B = 24°, ∠C = 30°
So the shortest side is opposite ∠B, followed by opposite ∠C, followed by opposite ∠A
So: AC, AB, BC
11. For a triangle to "work", two sides cannot add up to less than the third side.
Think of a "triangle" that looked like this:
/-------------------\
where the left and right sides were of length 1, and the base was length 20. It can't be a triangle!
So, only the second one can be a triangle (the last one is actually a straight line!)
12. From this it follows that "At least 7" is not good enough - seven would again give a straight line.
And "at most 19" is not good enough - nineteen would again give a straight line.
So you want "Greater than 7 and less than 19"