Hey could someone please help me with this really hard assignment is taking me forever. Thank you marking brainliest!

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)

146%

step-by-step explanation: