Aylissa plans to use four triangles like the one shown to form a diamond shape.For her plan to work, the triangle must be a right triangle. Determine whether the triangle is a right triangle. Show your work.(1 point)

Question

6,4,3

Answer 1

To determine whether a triangle with side lengths 6, 4, and 3 is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem 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.

1. First, identify the lengths of the sides:

   • The sides are 6, 4, and 3.
   • The longest side is 6, so we will assume that this is the hypotenuse (c).

2. Next, we square the lengths of the sides:

   • \(c^2 = 6^2 = 36\)
   • \(a^2 = 4^2 = 16\)
   • \(b^2 = 3^2 = 9\)

3. Now, use the Pythagorean theorem: \[ c^2 = a^2 + b^2 \] Substitute the values we found: \[ 36 = 16 + 9 \] Simplifying the right side: \[ 36 = 25 \] This is not true. Therefore, the equation does not hold.

Since the sum of the squares of the two shorter sides (16 + 9 = 25) does not equal the square of the longest side (36), we conclude that the triangle with sides 6, 4, and 3 is not a right triangle.