Question
A carpenter is measuring a cabinet to ensure the sides create a right angle.
the distances are 4 ,3 and 5
Determine whether the triangle is a right triangle.
the distances are 4 ,3 and 5
Determine whether the triangle is a right triangle.
Answers
GPT-4o mini
To determine whether the triangle formed by the sides measuring 3, 4, and 5 units is a right triangle, we can use the Pythagorean theorem. According to the theorem, for a triangle with sides \(a\), \(b\), and \(c\), where \(c\) is the length of the longest side, the triangle is a right triangle if:
\[ a^2 + b^2 = c^2 \]
In this case, let's identify the sides:
- The longest side \(c\) is 5.
- The other sides \(a\) and \(b\) are 3 and 4.
Now we can plug these values into the theorem:
\[
3^2 + 4^2 = 5^2
\]
Calculating each term:
\[
9 + 16 = 25
\]
Simplifying the left side:
\[
25 = 25
\]
Since the equation holds true, the triangle with sides 3, 4, and 5 is indeed a right triangle.
\[ a^2 + b^2 = c^2 \]
In this case, let's identify the sides:
- The longest side \(c\) is 5.
- The other sides \(a\) and \(b\) are 3 and 4.
Now we can plug these values into the theorem:
\[
3^2 + 4^2 = 5^2
\]
Calculating each term:
\[
9 + 16 = 25
\]
Simplifying the left side:
\[
25 = 25
\]
Since the equation holds true, the triangle with sides 3, 4, and 5 is indeed a right triangle.