Question

is the triangle below a right triangle? remember, it might not be drawn to scale. use the pythagorean theorem to check. you can solve on paper and then enter your answer on zearn.
if the sides of a triangle, a, b, and c, make the equation (a^2 + b^2 = c^2) true, then the triangle is a right triangle and the longest side, c, is the hypotenuse.
the triangle (square) a right triangle.
the sum of the squares of the shorter sides, (a^2 + b^2), (square) the square of the longest side, (c^2).
(the triangle has sides 2.4, 3.2, 4)

Explanation:

Step1: Identify sides

Let \( a = 2.4 \), \( b = 3.2 \), \( c = 4 \) (longest side).

Step2: Calculate \( a^2 + b^2 \)

\( a^2 = 2.4^2 = 5.76 \), \( b^2 = 3.2^2 = 10.24 \)
\( a^2 + b^2 = 5.76 + 10.24 = 16 \)

Step3: Calculate \( c^2 \)

\( c^2 = 4^2 = 16 \)

Step4: Compare

Since \( a^2 + b^2 = c^2 \) (16 = 16), the triangle satisfies the Pythagorean Theorem.

Answer:

The triangle \(\boldsymbol{\text{is}}\) a right triangle.
The sum of the squares of the shorter sides, \(a^2 + b^2\), \(\boldsymbol{\text{equals}}\) the square of the longest side, \(c^2\).