Question

Nadia says the hypotenuse of this right triangle has a length of 73 because the Pythagorean theorem states that (28 + 45) squared = 73 squared.

3 squares are positioned to form a right triangle. The small square is labeled 28, medium square is 45, and large square is not labeled.

Which best describes Nadia’s solution?
She is correct because she applied the Pythagorean theorem properly and her arithmetic is accurate.
She is incorrect because she should have used 45 as the length of the hypotenuse.
She is incorrect because she should have squared each leg length and then found the sum.
She is correct because the hypotenuse is the longest side of the triangle.

Answer 1

Nadia's solution is incorrect because she should have squared each leg length and then found the sum.

According to the Pythagorean theorem, for a right triangle with legs of lengths \(a\) and \(b\) and a hypotenuse of length \(c\), the relationship is given by:

\[
a^2 + b^2 = c^2
\]

In this case, the legs are 28 and 45, so the correct equation would be:

\[
28^2 + 45^2 = c^2
\]

Calculating this gives:

\[
28^2 = 784 \quad \text{and} \quad 45^2 = 2025
\]
\[
784 + 2025 = 2809
\]

Now, to find \(c\):

\[
c = \sqrt{2809} = 53
\]

So, her claim that the hypotenuse is 73 is incorrect. The correct hypotenuse length is 53.