Cade and Tyce both tried to find the missing side of the right triangle.
A right triangle is shown. The legs are labeled 6 and 9. A right angle is labeled in between them.
Cade's Work Tyce's Work
a2 + b2 = c2 a2 + b2 = c2
62 + b2 = 92 62 + 92 = c2
36 + b2 = 81 36 + 81 = c2
b2 = 45 117 = c2
Square root b squared equals square root 45. Square root 117 equals c squared.
b ≈ 6.71 10.82 ≈ c
Is either of them correct? Explain your reasoning. (5 points)
Cade's work is correct.
He correctly applied the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c).
Cade correctly substituted the values of a (6) and b (9) into the equation a² + b² = c², and solved for b. By subtracting 36 from both sides of the equation, he obtained b² = 45. Taking the square root of both sides, he correctly found that b ≈ 6.71.
On the other hand, Tyce's work is incorrect.
Tyce mistakenly added the values of a (6) and b (9) and equated it to c², without squaring them. This is not the correct application of the Pythagorean theorem. Furthermore, Tyce incorrectly square rooted the result of adding 36 and 81, instead of the value of c². Consequently, Tyce's answer of 10.82 for c is incorrect.