Question

find p.

write your answer in simplest radical form.
kilometers
submit

Explanation:

Step1: Identify the triangle type

This is a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the hypotenuse \(c\) is \(\sqrt{2}\) times the length of each leg (\(a = b\)). Let the length of each leg be \(p\) (since the two non - hypotenuse sides are equal in a \(45 - 45-90\) triangle) and the hypotenuse \(c = 2\sqrt{2}\) km.
The formula for the relationship between the hypotenuse \(c\) and a leg \(a\) (or \(b\)) in a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle is \(c=a\sqrt{2}\).

Step2: Solve for \(p\)

We know that \(c = 2\sqrt{2}\) and \(c=p\sqrt{2}\). Substitute \(c\) into the formula:

$$
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$$

Answer:

\(2\) kilometers