Question
7cm 13cm 14cm
Is this a right triangle? Why or Why not?
(1 point)
Responses
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse
Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse
Is this a right triangle? Why or Why not?
(1 point)
Responses
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse
Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse
Answers
GPT-4o mini
To determine if the triangle with sides 7 cm, 13 cm, and 14 cm is a right triangle, we can use the Pythagorean Theorem. The theorem states that for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let’s assume 14 cm is the hypotenuse. We will check if the following condition holds true:
\[ c^2 = a^2 + b^2 \]
Where:
- \( c = 14 \) cm (hypotenuse)
- \( a = 7 \) cm
- \( b = 13 \) cm
Calculating:
\[
14^2 = 196
\]
\[
7^2 + 13^2 = 49 + 169 = 218
\]
Since \( 196 \neq 218 \), the Pythagorean Theorem does not hold true with 14 cm as the hypotenuse.
Now, testing if 13 cm could be the hypotenuse:
\[
13^2 = 169
\]
\[
7^2 + 14^2 = 49 + 196 = 245
\]
Since \( 169 \neq 245 \), the theorem does not hold with 13 cm as the hypotenuse either.
Testing 7 cm as the hypotenuse is not valid since it is the smallest side.
Thus, the only conclusion is:
**No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse.**
Let’s assume 14 cm is the hypotenuse. We will check if the following condition holds true:
\[ c^2 = a^2 + b^2 \]
Where:
- \( c = 14 \) cm (hypotenuse)
- \( a = 7 \) cm
- \( b = 13 \) cm
Calculating:
\[
14^2 = 196
\]
\[
7^2 + 13^2 = 49 + 169 = 218
\]
Since \( 196 \neq 218 \), the Pythagorean Theorem does not hold true with 14 cm as the hypotenuse.
Now, testing if 13 cm could be the hypotenuse:
\[
13^2 = 169
\]
\[
7^2 + 14^2 = 49 + 196 = 245
\]
Since \( 169 \neq 245 \), the theorem does not hold with 13 cm as the hypotenuse either.
Testing 7 cm as the hypotenuse is not valid since it is the smallest side.
Thus, the only conclusion is:
**No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse.**