Question

If a triangle has sides measuring 60 in., 75 in., and 45 in. in
length, is it a right triangle?
*Hint: Use the converse of the Pythagorean Theorem to check.
Don't forget to use your Desmos calculator and STAAR Reference
Sheet to help!
(1 point)
No, because 9,225 does not equal 2,025.
Yes, because 3,600 equals 3,600.
No, because 5,625 does not equal 3,600.
Yes, because 5,625 equals 5,625.

Answer 1

To determine whether the triangle with sides measuring 60 in., 75 in., and 45 in. is a right triangle, we can use the converse of the Pythagorean theorem. According to this theorem, in a right triangle, if \( c \) is the length of the hypotenuse (the longest side), and \( a \) and \( b \) are the lengths of the other two sides, then it must hold that:

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

1. Identify the lengths of the sides. The longest side is 75 in., so:
- \( c = 75 \) in.
- \( a = 60 \) in.
- \( b = 45 \) in.

2. Calculate the squares of the sides:
- \( c^2 = 75^2 = 5625 \)
- \( a^2 = 60^2 = 3600 \)
- \( b^2 = 45^2 = 2025 \)

3. Now, check if the Pythagorean theorem holds:
- \( a^2 + b^2 = 3600 + 2025 = 5625 \)

4. Now compare \( c^2 \) with \( a^2 + b^2 \):
- \( c^2 = 5625 \)
- \( a^2 + b^2 = 5625 \)

Since \( c^2 = a^2 + b^2 \), the condition for a right triangle is satisfied.

The answer is:

**Yes, because 5,625 equals 5,625.**