Question

Use the Pythagorean Theorem to determine which of the following give the measures of the legs and hypotenuse of a right triangle. Check all that apply.
A. 3, 4, 5
B. 4, 11, 14
C. 9, 14, 17
D. 8, 14, 16
E. 8, 15, 17

Answer 1

The Pythagorean theorem states that the square of the hypotenuse is equal to  the sum of the squares of the legs:

$c^2=a^2+b^2.$

The hypotenuse is the side with the greatest length.

Check all options:

1. c=5, a=3, b=4:

$5^2=25,\\3^2+4^2=9+16=25,\\5^2=3^2+4^2$ true.

2. c=14, a=4, b=11:

$14^2=196,\\4^2+11^2=16+121=137,\\14^2\neq 4^2+11^2$ false.

3. c=17, a=9, b=14:

$17^2=289,\\9^2+14^2=81+196=277,\\17^2\neq 9^2+14^2$ false.

4. c=16, a=8, b=14:

$16^2=256,\\8^2+14^2=64+196=260,\\16^2\neq 8^2+14^2$ false.

5. c=17, a=8, b=15:

$17^2=289,\\8^2+15^2=64+225=289,\\17^2=8^2+15^2$ true.

Answer: correct options are A and E.

Answer 2

Using the Pythagorean Theorem the measures of the legs and hypotenuse of a right angled triangles are;

A. 3, 4, 5

E. 8, 15, 17

Further Explanation;

Pythagoras theorem

• Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs.
• Therefore; if the legs of a right-angled triangle are a and b and the hypotenuse is c, then: $a^{2} + b^{2} = c^{2}$

In this case;

Options A and E are correct because they obey the Pythagoras theorem;

1.Option A

3, 4, 5

$a= 3, b=4, and c= 5$

Therefore using Pythagoras theorem;

$a^{2} + b^{2} = c^{2}$

Replacing the variables

$3^{2} + 4^{2} = 5^{2}$

$9 + 16 = 25 = c^{2}$ (True)

2. Option e

8, 15, 17

$a= 8, b=15, and c= 17$

Therefore using Pythagoras theorem;

$a^{2} + b^{2} = c^{2}$

Replacing the variables

$8^{2} + 15^{2} = 17^{2}$

$64 + 225= c^{2} = 289$ (True)

Options B and C are incorrect because they don't follow the Pythagoras theorem.

1. Option B

$a= 4, b=11, and c= 14$

Therefore using Pythagoras theorem;

$a^{2} + b^{2} = c^{2}$

Replacing the variables

$4^{2} + 11^{2} = 14^{2}$

$16+ 121 = 137 ≠ c^{2}$ (False)

2. Option C

$a= 9, b=14, and c= 17$

Therefore using Pythagoras theorem;

$a^{2} + b^{2} = c^{2}$

Replacing the variables

$9^{2} + 14^{2} = 17^{2}$

$c^{2} = 289$

$81 + 196 = 277 ≠ c^{2}$ (False)

3. Option D

$a= 8, b=15, and c= 16$

Therefore using Pythagoras theorem;

$a^{2} + b^{2} = c^{2}$

Replacing the variables

$8^{2} + 15^{2} = 16^{2}$

$c^{2} = 256$

$64 + 225 = 289 ≠ c^{2}$ (False)

Keywords: Right triangle, Pythagoras theorem

Learn more about:  

• Pythagoras theorem: brainly.com/question/4098846
• Right triangle: brainly.com/question/4098846

Level; High school  

Subject: Mathematics  

Topic: Pythagoras theorem