Find the lower bound for the following lengths:
1 answer:
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Answer:
Exercise 1: The length of the unknown leg is 4 inches.
Exercise 3: The following straws can be used to construct the triangle: b) , c)
, d)
, e)
, f)
Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)
Step-by-step explanation:
Exercise 1:
Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:
(1)
Where:
- Hypotenuse, in inches.
- Known leg, in inches.
- Unknown leg, in inches.
If we know that and
, then the length of the unknown leg is:
Since 4 is the least whole number closest to , then we conclude that the length of the unknown leg is 4 inches.
Exercise 3:
The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:
(2)
Where:
- Greater side, in inches.
- Lesser side, in inches.
- Missing side, in inches.
If we know that and
, then we have the following range of missing sides:
The following straws can be used to construct the triangle: b) , c)
, d)
, e)
, f)
Exercise 4:
Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:
(i)
Possible choices: 5 inches.
(ii)
Possible choices: 4 inches, 6 inches.
(iii)
Possible choices: 5 inches, 6 inches.
(iv)
Possible choices: None.
(v)
Possible choices: 2 inches, 6 inches.
(vi)
Possible choices: 5 inches.
(vii)
Possible choices: None.
(viii)
Possible choices: 2 inches, 4 inches, 10 inches.
(ix)
Possible choices: 6 inches.
(x)
Possible choices: 5 inches.
Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)