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) The triangle a right triangle. at the top 6cm at the left 3cm and at the bottem 4cm

Question

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) The triangle a right triangle. at the top 6cm   at the left 3cm and at the bottem 4cm

GPT-4o mini · Answer

To determine if the triangle with sides of 6 cm, 3 cm, and 4 cm is a right triangle, we can use the Pythagorean theorem, which states:

$a^{2} + b^{2} = c^{2}$

where $c$ is the length of the hypotenuse (the longest side), and $a$ and $b$ are the lengths of the other two sides.

From the given dimensions:

The sides are 6 cm, 3 cm, and 4 cm.
The longest side is 6 cm, so we will consider it as $c$ .
Therefore, $a = 4$ cm and $b = 3$ cm.

Now, we can plug in the values:

$4^{2} + 3^{2} = 6^{2}$

Calculating the squares:

$16 + 9 = 36$

Now, add the values on the left side:

$25 \neq 36$

Since $25$ is not equal to $36$ , the triangle with sides 6 cm, 3 cm, and 4 cm does not satisfy the Pythagorean theorem and therefore is not a right triangle.