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

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. According to this theorem, for a triangle to be a right triangle, the square of the length of the longest side (hypotenuse) must equal the sum of the squares of the lengths of the other two sides.

1. Assign the sides:
- Let's take 50 cm as the longest side (hypotenuse).
- The other sides are 40 cm and 32 cm.

2. Apply the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \( c \) is the hypotenuse.

3. Calculate:
- \( 40^2 + 32^2 \):
\[
40^2 = 1600
\]
\[
32^2 = 1024
\]
\[
40^2 + 32^2 = 1600 + 1024 = 2624
\]

- \( 50^2 \):
\[
50^2 = 2500
\]

4. Compare:
\[
40^2 + 32^2 = 2624 \quad \text{and} \quad 50^2 = 2500
\]

Since \( 2624 \neq 2500 \), triangle DEF is **not** a right triangle.

Therefore, the answer is **False**.