Question

hanss work
$9^{2}+40^{2}=c^{2}$
$81 + 80 = c^{2}$
$161 = c^{2}$
$sqrt{161}mathrm{cm}=c$
hans wanted to find the length of the hypotenuse of the triangle. which statement correctly identifies his error?
he did not finish the problem. he should have divided 161 by 2 to find the square root.
he should have added $9 + 9$ to find the value of $9^{2}$.
he should have subtracted the two squares to get $40^{2}-9^{2}=c^{2}$ because numbers get too large if both legs are squared and then added together.
he did not square 40, he just multiplied by 2.

Explanation:

Step1: Analyze \(40^{2}\)

According to the formula \(a^{2}=a\times a\), \(40^{2}=40\times40 = 1600\), not \(40\times2=80\).

Step2: Analyze other options

• Option 1: The square - root of \(x\) is \(\sqrt{x}\), not \(\frac{x}{2}\). For example, \(\sqrt{16}=4

eq\frac{16}{2} = 8\).

• Option 2: \(9^{2}=9\times9=81

eq9 + 9=18\).

• Option 3: In a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), by the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), not \(a^{2}-b^{2}=c^{2}\).

Answer:

He did not square \(40\), he just multiplied by \(2\).