Question
Is this a right triangle? Side lengths of 4 in., 6 in., and 9 inches.
No
Yes
No
Yes
Answers
Answered by
GPT-4o mini
To determine if a triangle with side lengths of 4 inches, 6 inches, and 9 inches is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Here, the longest side is 9 inches. We will check if the following equality holds:
\[
\text{Hypotenuse}^2 = \text{Side}_1^2 + \text{Side}_2^2
\]
Substituting the values:
\[
9^2 = 4^2 + 6^2
\]
Calculating each side:
\[
81 = 16 + 36
\]
Now, adding the sides on the right:
\[
81 = 52
\]
Since \(81 \neq 52\), the triangle with sides of 4 inches, 6 inches, and 9 inches is **not a right triangle**.
So the answer is:
**No**.
Here, the longest side is 9 inches. We will check if the following equality holds:
\[
\text{Hypotenuse}^2 = \text{Side}_1^2 + \text{Side}_2^2
\]
Substituting the values:
\[
9^2 = 4^2 + 6^2
\]
Calculating each side:
\[
81 = 16 + 36
\]
Now, adding the sides on the right:
\[
81 = 52
\]
Since \(81 \neq 52\), the triangle with sides of 4 inches, 6 inches, and 9 inches is **not a right triangle**.
So the answer is:
**No**.