Question

question 12
find the remaining sides of a 45° - 45° - 90° triangle if the longest side is 5√2. answer exactly.
both shorter sides:

Explanation:

Step1: Recall side - length ratio

In a 45° - 45° - 90° triangle, the ratio of the sides is \(a:a:a\sqrt{2}\), where \(a\) is the length of each of the two equal - length legs and \(a\sqrt{2}\) is the length of the hypotenuse.

Step2: Set up an equation

Let the length of each of the shorter sides be \(x\). The hypotenuse \(c = 5\sqrt{2}\), and since \(c=x\sqrt{2}\), we have the equation \(x\sqrt{2}=5\sqrt{2}\).

Step3: Solve for \(x\)

Divide both sides of the equation \(x\sqrt{2}=5\sqrt{2}\) by \(\sqrt{2}\). So \(x = 5\).

Answer:

5