C. 9 square roots of 2
To answer this question, it's super important that you understand the ratio of sides for special triangles. This triangle in particular, a 45-45-90 triangle, has a ratio between the legs and hypotenuse of 1:1:
Since we are given the value of the hypotenuse, we know that the value of the two sides multiplied by [tex]\sqrt{2}[/tex] will be 18. Knowing this, we can write out an equation:
u*[tex]\sqrt{2}[/tex] = 18
u = [tex]\frac{18}{\sqrt{2} }[/tex]
Multiply both sides by [tex]\sqrt{2}[/tex] in order to get rid of the root in the denominator:
u = [tex]\frac{18*\sqrt{2}}{\sqrt{2} * \sqrt{2}}[/tex]
u = [tex]\frac{18*\sqrt{2} }{2}[/tex]
u = 9[tex]\sqrt{2}[/tex]
If you'd like me to explain how I got to the answer any further, just ask!
- breezyツ
