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: https://brainly.com/question/4098846
- Right triangle: https://brainly.com/question/4098846
Level; High school
Subject: Mathematics
Topic: Pythagoras theorem
