Certainly! Let's solve this step-by-step.
In a 45-45-90 right triangle, the sides have a special relationship. A 45-45-90 triangle is an isosceles right triangle, and the ratio of the lengths of its sides is always [tex]\(1:1:\sqrt{2}\)[/tex]. This means that if both legs have the same length, [tex]\(x\)[/tex], the hypotenuse will be [tex]\(x\sqrt{2}\)[/tex].
Given:
- The legs of the triangle both have a length of 8 units.
Using the special ratio for a 45-45-90 triangle, where the hypotenuse is [tex]\(x\sqrt{2}\)[/tex]:
- Let [tex]\( x = 8 \)[/tex].
- Therefore, the hypotenuse length is [tex]\( 8\sqrt{2} \)[/tex].
Now, let's check this numerically:
- [tex]\( 8\sqrt{2} \approx 8 \times 1.414213562 \approx 11.313708498984761 \)[/tex].
The correct answer is:
D. [tex]\( 8\sqrt{2} \)[/tex] units
