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.(1 point)

Question

6,4,3

Answer 1

To determine whether the triangle with side lengths 6, 4, and 3 is a right triangle, we can use the Pythagorean theorem. According to the theorem, a triangle is a right triangle if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

1. Identify the longest side:

   • The sides are 6, 4, and 3.
   • The longest side is 6.

2. Apply the Pythagorean theorem:

   • According to the theorem: \( c^2 = a^2 + b^2 \)
   • Here, \( c = 6 \), \( a = 4 \), and \( b = 3 \).

Now, calculate:

• \( c^2 = 6^2 = 36 \)
• \( a^2 + b^2 = 4^2 + 3^2 = 16 + 9 = 25 \)

3. Check if \( c^2 = a^2 + b^2 \):
   • \( 36 \neq 25 \)

Since \( c^2 \) (36) does not equal \( a^2 + b^2 \) (25), the triangle with side lengths 6, 4, and 3 is not a right triangle.