Question

6 which of the following is the length of the missing side in the illustration below? image of a right triangle with one leg labeled 3cm and the other 4cm options: 25 cm, 3 cm, 5 cm, 4.3 cm

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle with legs of lengths \(a = 3\space cm\) and \(b = 4\space cm\). We use the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\) to find the hypotenuse (the missing side).

Step2: Apply the Pythagorean theorem

Substitute \(a = 3\) and \(b = 4\) into the formula:
\(c^{2}=3^{2}+4^{2}=9 + 16=25\)

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{25} = 5\space cm\)

Answer:

5 cm