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

Answer 1

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**.