If a triangle has sides measuring 60 in., 75 in., and 45 in. in

Question

length, is it a right triangle?
*Hint: Use the converse of the Pythagorean Theorem to check.
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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.