Question

value: 2
in the image below, $5\sqrt{2}$ is a leg of the 45 - 45 - 90 triangle.
true
false
#5/6

Explanation:

Step1: Recall 45 - 45 - 90 triangle properties

In a 45 - 45 - 90 triangle, the two legs are congruent. Let the length of each leg be \(a\) and the length of the hypotenuse be \(c\). The ratio of the sides is \(a:a:c = 1:1:\sqrt{2}\), or \(c = a\sqrt{2}\).

Step2: Analyze the given triangle

If one leg has a length of \(5\sqrt{2}\), and the other legs \(x\) and \(y\) should have the same length in a 45 - 45 - 90 triangle. Since the side labeled \(5\sqrt{2}\) is not the hypotenuse (the hypotenuse would be \(5\sqrt{2}\times\sqrt{2}=10\)), it is a leg.

Answer:

True