Question

A triangular piece of glass has sides that measure 33 in.,57 in., and 65 in. Is the piece of glass in the shape of a right triangle?

1. True
2. False

Answer 1

The triangular piece of glass with sides measuring 33 in., 57 in., and 65 in. is not a right triangle, as the sum of the squares of the shorter sides does not equal the square of the longest side according to the Pythagorean theorem.

Step-by-step explanation:

To determine if a triangular piece of glass with sides that measure 33 in., 57 in., and 65 in. 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 side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

For the given measurements, if the glass is a right triangle, then 572 + 332 should equal 652. Calculating these:

• 572 = 3249
• 332 = 1089
• 652 = 4225

Adding the squares of the shorter sides:

3249 + 1089 = 4338

Since 4338 does not equal 4225, the square of the longest side, the triangular piece of glass is not a right triangle. Therefore, the answer is False.