True or False

Question

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)
True
False

Answer 1

To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Here, the sides of triangle DEF measure:

• 50 cm (hypotenuse candidate)
• 40 cm
• 32 cm

1. Let's identify the longest side:

   • Longest side = 50 cm
   • Other sides = 40 cm and 32 cm

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

3. We can check: \[ 40^2 + 32^2 = 50^2 \] Calculating each:

   • \(40^2 = 1600\)
   • \(32^2 = 1024\)
   • \(50^2 = 2500\)

4. Adding the squares of the legs: \[ 1600 + 1024 = 2624 \]

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

So the answer is False.