Answer:
D
Step-by-step explanation:
A triangle with the angles of 45, 45, and 90 will have equivalent side lengths and a hypotenuse longer than them by a factor of [tex]\sqrt{2}[/tex]. If the area of the triangle is 25.5 square centimeters, then you can find the lengths of the sides of the triangle. Since the area of a triangle is the base multiplied by the height and then divided by 2, the side lengths of the triangle must be [tex]\sqrt{25.5\cdot 2}=\sqrt{51}[/tex]. This means that the hypotenuse of the triangle must be [tex]\sqrt{51}\cdot \sqrt{2}=\sqrt{102}[/tex], or a little over 10cm. Therefore, the answer I would pick is choice D. Hope this helps!
