A triangle has sides with lengths of 18 inches, 47 inches, and 54 inches. Is it a right triangle?

To determine if a triangle is a right triangle, we can use the **Pythagorean Theorem**, which states that for a right triangle, the square of the longest side (the hypotenuse) should be equal to the sum of the squares of the other two sides.

For a triangle with sides \(a\), \(b\), and \(c\) where \(c\) is the longest side, the theorem is:

\[
a^2 + b^2 = c^2
\]

Here, the sides of the triangle are 18 inches, 47 inches, and 54 inches. Since 54 is the longest side, we assume that it's the hypotenuse \(c\). Let's check if the Pythagorean Theorem holds:

1. \(a = 18\)
2. \(b = 47\)
3. \(c = 54\)

Now, let's compute:

\[
a^2 + b^2 = 18^2 + 47^2 = 324 + 2209 = 2533
\]

\[
c^2 = 54^2 = 2916
\]

Since \( a^2 + b^2 = 2533 \) and \( c^2 = 2916 \), the sum of the squares of the two smaller sides does **not** equal the square of the longest side.

Therefore, the triangle is **not a right triangle**.

Would you like further details or explanations? 

Here are some related questions:
1. How can you determine the type of triangle based on side lengths?
2. What is the significance of the Pythagorean Theorem in geometry?
3. Can any set of three side lengths form a triangle?
4. How can you determine if a triangle is obtuse or acute using side lengths?
5. What is Heron's formula for calculating the area of any triangle?

**Tip:** The Pythagorean Theorem applies only to right triangles; use it to verify if given side lengths form a right triangle!

Determine if a triangle with sides of 18 inches, 47 inches, and 54 inches is a right triangle using the Pythagorean Theorem. This problem involves checking the relationship between the side lengths using the formula a^2 + b^2 = c^2. Suitable for students in Grades 7-9.

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