Question

9 which of the following is the length of the missing side in the illustration below? image of a red right triangle with hypotenuse labeled 5 cm and one leg labeled 3 cm options: 4 cm, 9 cm, 16 cm, 4.3 cm

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle (since one angle is a right angle, as it's a right - angled triangle with hypotenuse 5 cm and one leg 3 cm). We can use the Pythagorean theorem, which states that for a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(c^{2}=a^{2}+b^{2}\). Let the missing side be \(a\), the given leg \(b = 3\) cm and hypotenuse \(c = 5\) cm.

Step2: Apply the Pythagorean theorem

We want to find \(a\), so we can re - arrange the formula \(c^{2}=a^{2}+b^{2}\) to \(a^{2}=c^{2}-b^{2}\). Substitute \(c = 5\) and \(b = 3\) into the formula: \(a^{2}=5^{2}-3^{2}\). Calculate \(5^{2}=25\) and \(3^{2}=9\), so \(a^{2}=25 - 9=16\). Then take the square root of both sides: \(a=\sqrt{16}=4\) cm.

Answer:

4 cm (corresponding to the option "4 cm")