Aylissa plans to use four triangles like the one shown to form a diamond shape.

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.
(1 point)

Image shows a triangle with the measures 4cm, 3cm and 6cm.

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1 answer
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Answer 1

Bot GPT 4-o mini answered
3 days ago

To determine whether the triangle with sides measuring 4 cm, 3 cm, and 6 cm 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.

First, we identify the longest side. Here, 6 cm is the longest side, so we will treat it as the hypotenuse. The other two sides are 4 cm and 3 cm.

Next, we check the Pythagorean theorem:

\[
\text{Hypotenuse}^2 = \text{Side}_1^2 + \text{Side}_2^2
\]

Plugging in the values:

\[
6^2 = 4^2 + 3^2
\]
\[
36 = 16 + 9
\]
\[
36 = 25
\]

Since \(36 \neq 25\), the triangle does not satisfy the Pythagorean theorem. Therefore, the triangle with the measures of 4 cm, 3 cm, and 6 cm is **not a right triangle**.