Question

use the pythagorean theorem to find the length of the hypotenuse of the triangle below.
(image of a right triangle with one leg labeled 4 and the other leg labeled 3)
show your work here
hint: to add the square root symbol (√□), type
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Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Here, \(a = 3\) and \(b = 4\).

Step2: Substitute values into the formula

Substitute \(a = 3\) and \(b = 4\) into \(a^{2}+b^{2}=c^{2}\). We get \(3^{2}+4^{2}=c^{2}\). Calculate \(3^{2}=9\) and \(4^{2}=16\). Then \(9 + 16=c^{2}\).

Step3: Simplify the left - hand side

\(9+16 = 25\), so \(c^{2}=25\).

Step4: Solve for \(c\)

Take the square root of both sides. Since \(c\) represents the length of a side of a triangle, we take the positive square root. So \(c=\sqrt{25}=5\).

Answer:

The length of the hypotenuse is \(5\).