Complete Question:
Jocelyn said that the triangle below is not a right triangle. Her work is shown below. Explain what she did wrong, and show Jocelyn the correct solution.
We need to check if 27² + 45² = 36² is a true statement. The left side of the equation is equal to 2,754. The right side of the equation is equal to 1,296. That means 272 + 452 = 362 is not true, and the triangle shown is not a right triangle
Answer/Step-by-step explanation:
Jocelyn used a wrong equation and statement.
Here's what she should have stated and done.
Using the converse of Pythagorean Theorem, which says that a triangle with sides a, b, and c is a right triangle if it satisfy the statement: a² + b² = c².
Where, c is the hypotenuse which is the longest leg. While a and b are the side lengths of the other two legs.
Therefore, in this case,
c = 45
b = 27
a = 36
Thus, what we need to check to be true would be:
36² + 27² = 45² (this is where Jocelyn made a mistake. Jocelyn wrote 27² + 45² = 36² rather)
Let's check if it's true.
2,025 = 2,025 (this is true)
Therefore, the triangle is a right triangle.
