Question

1. in a right triangle, if the legs are equal in length, and each is √2, what is the hypotenuse?

a. 1
b. √3
c. 2
d. √5

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse.

Step2: Substitute the values of \(a\) and \(b\)

Given \(a = b=\sqrt{2}\), then \((\sqrt{2})^{2}+(\sqrt{2})^{2}=c^{2}\).

Step3: Calculate the left - hand side

\((\sqrt{2})^{2}=2\), so \(2 + 2=c^{2}\), which means \(c^{2}=4\).

Step4: Solve for \(c\)

Taking the square root of both sides, \(c=\sqrt{4}=2\) (we take the positive value since length cannot be negative).

Answer:

C. 2