100 points 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?

Part B: The second link is for this part

(d) The front of the stage, side C, is 50 feet long. A 40-foot rope runs along the side of square B. A 30-foot rope runs along the side of square A. Is the roped off area, triangle ABC, a right triangle? Explain.

(e) The diagonal of square A, marked off by the red stars, is where the concession stand is located. A local high school band is performing at the outdoor theater on a summer evening. The band has a school banner that is 40-feet long, and band members would like to hang it across the concession stand to let people know they are performing. Estimate the length of the concession stand to determine if the school banner can fit across the length of the concession stand. Show your work and explain your reasoning.