Question

16√22
x
45°

Explanation:

Step1: Identify the triangle type

This is a \(45^{\circ}-45^{\circ}-90^{\circ}\) right - triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the sides are in the ratio \(1:1:\sqrt{2}\). Let the legs be of length \(a\) and the hypotenuse be \(c\). The formula is \(c = a\sqrt{2}\).

Step2: Apply the formula

Here, one leg \(a = 16\sqrt{22}\), and we need to find the hypotenuse \(x\). Using the formula \(x=a\sqrt{2}\), substitute \(a = 16\sqrt{22}\) into it.

$$x=16\sqrt{22}\times\sqrt{2}$$

$$x = 16\sqrt{44}$$

$$x=16\times2\sqrt{11}$$

$$x = 32\sqrt{11}$$

Answer:

\(x = 32\sqrt{11}\)