Question

Jeremy is trying to explain why a triangle with side lengths 35, 30, 60 is not a right triangle. His explanation is shown below.

Step 1: 35 squared + 30 squared question mark equals 60 squared
Step 2: (35 + 30) squared question mark equals 60 squared
Step 3: 65 squared question mark equals 60 squared
Step 4: 4,225 not-equals 3,600

Which best describes Jeremy’s explanation?
Jeremy’s explanation is accurate.
Jeremy’s explanation is inaccurate. He wrote the leg lengths in the incorrect order in step 1.
Jeremy’s explanation is inaccurate. He incorrectly combined terms in step 2.
Jeremy’s explanation is inaccurate. He multiplied incorrectly in step 4.

Answer 1

Jeremy's explanation of why a triangle with sides 35, 30, 60 is not a right triangle is inaccurate because he incorrectly combined the lengths of the sides in step 2 instead of applying the Pythagorean theorem correctly.

Step-by-step explanation:

Jeremy's explanation as to why a triangle with side lengths 35, 30, 60 is not a right triangle is inaccurate. In step 2 of his explanation, he incorrectly combines the lengths of two sides when he adds 35 and 30 and then squares the result. According to the Pythagorean theorem, for a triangle to be a right triangle, the sum of the squares of the two shorter sides (legs) must be equal to the square of the longest side (hypotenuse). The correct approach is to square each of the sides separately and then add them together to compare with the square of the hypotenuse.

Jermey's correct calculation should be: 35 squared + 30 squared does not equal 60 squared. Specifically, it should be:

1. 352 + 302 = 1,225 + 900 = 2,125,
2. 602 = 3,600,
3. 2,125 < 3,600, thus confirming that the given triangle is not a right triangle.

In mathematics, it is crucial to apply the Pythagorean theorem correctly to determine the nature of a triangle.