To find the length of one leg of a 45°-45°-90° triangle when the hypotenuse is given, we can use the properties of this special type of triangle.
A 45°-45°-90° triangle is an isosceles right triangle. This means the two legs are of equal length, and their lengths, when squared and summed together, equal the square of the hypotenuse according to the Pythagorean Theorem [tex]\( a^2 + a^2 = c^2 \)[/tex], where [tex]\( a \)[/tex] is the length of a leg and [tex]\( c \)[/tex] is the hypotenuse.
However, there's a direct formula for the lengths of the legs in a 45°-45°-90° triangle: each leg's length is [tex]\(\frac{c}{\sqrt{2}}\)[/tex].
Given that the hypotenuse [tex]\( c \)[/tex] is 18 cm, the length of each leg [tex]\( a \)[/tex] can be calculated as follows:
[tex]\[ a = \frac{18}{\sqrt{2}} \][/tex]
To rationalize the denominator:
[tex]\[ a = \frac{18}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{18\sqrt{2}}{2} = 9\sqrt{2} \][/tex]
So, the length of one leg of the triangle is [tex]\( 9\sqrt{2} \)[/tex] cm.
Thus, the correct answer is:
[tex]\[ 9 \sqrt{2} \text{ cm} \][/tex]
