A square is shown below. The length of the diagonal can be determined by using the Pythagorean Theorem.

1) Finda rationallength of one of the sides sidesthat results in a rational hypotenuse.

2) Find an irrational length of one of the sides sides that results in a rational hypotenuse.

Be sure to show the sum of each statement in simplest radical form.

2.Ariana has created a paper airplane for her physics class at school where all the students will be testing their planes by sending it off the third floor of the building. The physics teacher is requiring her paper airplane to swoop down at a single point to graze the ground before it rises back into the air. Her initial attempt is modeled by the function, h(x)=x²12x+35 wherehis the height in feet andxis the time in seconds of the paper airplanes path.

a) In how many seconds will the paper airplane crash into the ground?

3.A rocket is launched with an initial velocity of 100 ft/s. The height of the rocket in meters is modeled by the function shown below, where t is time in seconds.

h(t)=4t²+ 120t

Write a statement that describes the 1) domain of this function and 2) range of this function. Make sure to include an explanation as to why you know these values are included in the domain and in the range of the function.