Question

jerrod found the hypotenuse of a right triangle with legs 3 ft and 1 ft. is his answer correct?
jerrods work
$c^{2}=3^{2}+1^{2}$
$c^{2}=9 + 1$
$c^{2}=8$
$c=sqrt{8}$
no, he setup the pythagorean theorem incorrectly.
no, he made an error finding the square root.
no, he subtracted 1 and 9 instead of adding.
yes, he correctly calculated the length of the hypotenuse.

Explanation:

Step1: Recall the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Here \(a = 3\) and \(b=1\).

Step2: Calculate \(c^{2}\)

According to the Pythagorean theorem, \(c^{2}=3^{2}+1^{2}\). Since \(3^{2}=9\) and \(1^{2}=1\), then \(c^{2}=9 + 1=10\).

Step3: Analyze Jerrod's work

Jerrod calculated \(c^{2}=3^{2}+1^{2}=9 + 1\) correctly, but then he said \(c^{2}=8\) (he subtracted \(1\) from \(9\) instead of adding). The correct \(c=\sqrt{10}\), not \(\sqrt{8}\).

Answer:

No, he set up the Pythagorean theorem incorrectly.