Question

Use the Pythagorean theorem to determine if it’s a right triangle using sides 9.6 12.8 and 16.0

Answer 1

To determine if the triangle with sides 9.6, 12.8, and 16.0 is a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) should be equal to the sum of the squares of the lengths of the other two sides.

1. Identify the longest side:
- The sides are 9.6, 12.8, and 16.0. The longest side is 16.0.

2. Apply the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the longest side. In this case, \( a = 9.6 \), \( b = 12.8 \), and \( c = 16.0 \).

3. Calculate \( a^2 \), \( b^2 \), and \( c^2 \):
\[
a^2 = (9.6)^2 = 92.16
\]
\[
b^2 = (12.8)^2 = 163.84
\]
\[
c^2 = (16.0)^2 = 256.0
\]

4. Check if \( a^2 + b^2 = c^2 \):
\[
92.16 + 163.84 = 256.0
\]
\[
256.0 = 256.0
\]

Since the equation holds true, the triangle with sides 9.6, 12.8, and 16.0 is a right triangle.