On the southeast corner of Millennium Park, there is a garden walk. It is marked off in red in the drawing below. Side C, the hypotenuse of the triangle, shows the row along which flowers will be planted.
a) If side a measures 90 feet and side b measures 120 feet, how many feet of flowers will be planted along side c, the hypotenuse of the triangle? Show your work and explain your reasoning.
b) Calculate the area of the red triangle to find the area of the garden. Show your work.
c) Millennium Park has an outdoor concert theater. Before a concert, the area reserved for special seating is roped off in the shape of a triangle as shown below. How can the converse of the Pythagorean theorem help you determine whether the roped off area is in the shape of a right triangle?
