1. Remodeling is a Lengthy Process Bea Hind is remodeling her square family room by tearing down one wall and extending the room by 3 feet. The room will then be rectangular with an area of 180 square feet. What are the current dimensions of the family room?

2. Bea’s Original Family Room Addition = the length of one side of original room However, we cannot have a negative length to a room! Remember to check your answer :

3. Spears and FedX Need More Space Once upon a time when Brittany and her husband found out they were having another baby, they needed more space in their square living room. They decided to tear down one wall and extend the room by 2 feet. The room will then be rectangular with an area of 63 square feet. What are the current dimensions of the ex- Sears’ living room?

4. Brittany’s Original Family Room Addition = the length of one side of original room However, we cannot have a negative length to a room! Remember to check your answer :

5. You still gotta work… J Lo is still tutoring math to earn extra money. Her ex-boyfriend, P. Diddy, tests her math ability by giving her the following problem to solve: The square of a number minus twice the number is 48. Find the number.

6. A number squared minus twice the number is 48. Check your answer:

7. You still gotta work…continued Diddy cannot believe J Lo correctly answered his problem. He decided to give her a more challenging problem. He tells her that: The square of a number is twice the number minus one. Find the number.

8. A number squared is two times the number minus one. Check your answer:

9. The Return of…You still gotta work Diddy is truly amazed at J Lo’s mathematical ability as she correctly answered his second problem. He can’t believe that he ever let such a talented mathematician get away! He decides to give her one last problem. He tells her that: The sum of the squares of two consecutive odd positive integers is 650. She must find both integers.

10. (odd integer) 2 + (next odd integer) 2 = 650 First odd integer = Next odd integer = Not a positive integer.

11. Geometry Genius Betty Bye is designing a triangular piece of art. The base of the triangle is 2 inches less than the height. The area is 40 in 2. Find the length of the height and base.

12. Betty Bye is designing a triangular piece of art. The base of the triangle is 2 inches less than the height. The area is 40 in 2. Find the length of the height and base. h = height Cannot have a negative length.

13. Challenge!!! R. U. Nutts has a rectangular piece of cardboard that is twice as long as it is wide. Squares that are 2 cm on each side are cut out of each corner, and the ends are turned up to make a box whose volume is 480 cm 3. What are the original dimensions of the piece of cardboard?

14. x = width of cardboard