Question

True or False Triangle DEF has sides measuring 50 cm., 40 cm., and 32 cm. in length. It is a right triangle. Hint: Don't forget to use your Desmos calculator and STAAR Reference Sheet to help! (1 point) Responses True True False

Answer 1

To determine whether Triangle DEF with sides measuring 50 cm, 40 cm, and 32 cm is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that for a triangle to be a right triangle, the sum of the squares of the two shorter sides must equal the square of the longest side.

1. Identify the sides: 50 cm, 40 cm, and 32 cm.
2. The longest side is 50 cm.
3. Calculate the squares of the sides:
- \(50^2 = 2500\)
- \(40^2 = 1600\)
- \(32^2 = 1024\)

4. Calculate the sum of the squares of the two shorter sides:
\[
40^2 + 32^2 = 1600 + 1024 = 2624
\]

5. Compare this sum to the square of the longest side:
\[
50^2 = 2500
\]

Since \(2624 \neq 2500\), Triangle DEF does not satisfy the condition of the Pythagorean theorem.

Thus, the statement is **False**.