Question

find the length of the missing side. 20 cm, 48 cm. options: 42 cm, 48 cm, 25 cm, 52 cm

Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle (has a right - angle symbol). For a right - triangle, we can use the Pythagorean theorem, which 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, \(a = 20\space cm\) and \(b = 48\space cm\), and we need to find the hypotenuse \(c\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 20\) and \(b = 48\) into the formula \(c=\sqrt{a^{2}+b^{2}}\). First, calculate \(a^{2}\) and \(b^{2}\):
\(a^{2}=20^{2}=400\)
\(b^{2}=48^{2}=2304\)
Then, \(a^{2}+b^{2}=400 + 2304=2704\)
Now, find the square root of \(2704\): \(\sqrt{2704}=52\)

Answer:

52 cm