Question

what is the hypotenuse of this triangle?
2
3
?
select the best answer

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\). Here, \(a = 2\) and \(b = 3\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 2\) and \(b = 3\) into the formula. So \(c^{2}=2^{2}+3^{2}\). Calculate \(2^{2}=4\) and \(3^{2}=9\). Then \(c^{2}=4 + 9=13\). To find \(c\), we take the square root of both sides: \(c=\sqrt{13}\approx3.61\) (if we want a decimal approximation) or we can leave it as \(\sqrt{13}\). But since the problem is about identifying the hypotenuse length using the Pythagorean theorem, the length of the hypotenuse is \(\sqrt{2^{2}+3^{2}}=\sqrt{4 + 9}=\sqrt{13}\) (or approximately \(3.61\)).

Answer:

The length of the hypotenuse is \(\boldsymbol{\sqrt{13}}\) (or approximately \(3.61\))