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.



(1 point)
Responses

No, because 9,225 does not equal 2,025.
No, because 9,225 does not equal 2,025.

Yes, because 3,600 equals 3,600.
Yes, because 3,600 equals 3,600.

No, because 5,625 does not equal 3,600.
No, because 5,625 does not equal 3,600.

Yes, because 5,625 equals 5,625.

Answer 1

To determine if 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, which states that if a triangle is a right triangle, then the square of the length of the longest side (the hypotenuse) should equal the sum of the squares of the lengths of the other two sides.

First, we identify the longest side:
- 60 in.
- 75 in. (longest side)
- 45 in.

Now we apply the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
where \( c \) is the length of the longest side (75 in.), and \( a \) and \( b \) are the lengths of the other two sides (60 in. and 45 in.).

Calculate \( c^2 \):
\[
75^2 = 5625
\]

Calculate \( a^2 + b^2 \):
\[
60^2 + 45^2 = 3600 + 2025 = 5625
\]

Since \( c^2 = a^2 + b^2 \):
\[
5625 = 5625
\]

This confirms that the triangle is indeed a right triangle.

Based on the options provided, the correct response is:
**Yes, because 5,625 equals 5,625.**