Question

find the missing side of the triangle (theorem) 3cm 4cm

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 \(c\), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 3\space cm\) and \(b = 4\space cm\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 3\) and \(b = 4\) into the formula \(c=\sqrt{a^{2}+b^{2}}\). First, calculate \(a^{2}+b^{2}\): \(3^{2}+4^{2}=9 + 16=25\). Then, take the square root of the result: \(c=\sqrt{25}=5\).

Answer:

The length of the missing side (hypotenuse) is \(5\space cm\).