1. Find a number (or numbers) that is (are) 110 less than its square.

2. The sum of the squares of two consecutive odd numbers is 74. Find the numbers. Hint: there may be more than one set.

3. The difference between a number and its square is thirty. Find the number.

4. The length of a rectangle is one less than twice the width. Find the dimensions of the rectangle if the area is 153 square feet.

5. Konstantin Levin’s field has a perimeter of 38 meters and an area of 88 square meters. Find the dimensions.

6. The perimeter of an index card is 20 inches and the area is 24 square inches. What are the dimensions of the card?

7. The perimeter of a bedroom is 44 feet and the area is 120 square feet. What are the dimensions of the bedroom?

8. Two planes leave BWI; one flies North and one flies West. Later in the day, the planes are 25 miles apart. The North-bound plane is 17 miles farther away from BWI than the West-bound. How far has each plane traveled?

9. A thirteen foot ladder leans against Jericho’s wall to reach Rahab’s window. The top of the ladder is seven feet farther from the base of the wall than the bottom. How high is the window?

10. Two surveyors are 17 yards apart. One is due south of a post and another is due west. If one surveyor is 7 yards farther from the post than the other, how far is each surveyor from the post?

12. Jack’s patio is eight feet by eleven feet. He plans to enlarge it by adding the same amount to each dimension. If the new patio will be one hundred thirty square feet, how much did he add to each side?

13. Will has a garden that is 12 feet by 15 feet. He wants to increase the area of the garden by 90 square feet by increasing each dimension by the same amount. What are the dimensions of his new garden?

14. As part of the April Fool’s prank, the seniors plan to build a pen to house the freshmen. They will use the Northern Parkway wall as one side and 200 feet of razor wire as the other three sides. If the area of the pen is 3,750 square feet, what are the dimensions?

15. In retaliation, the freshmen build a fence to impound the seniors’ cars. They use the curb as one wall and 100 feet of fencing for the other three. If the area of the pen is 1,200 square feet, find the dimensions of the pen.

16. Sam wants to design a new back yard. The plot of land is six yards by eight yards. He plans to have a rectangular pool surrounded by a sand walkway that is the same width all the way around. If the area of the pool and the walkway are the same, what are the dimensions of the pool?

17. Fredo’s Framers want to frame Sonny’s diploma from Furman University. The frame will be 20 inches by 34 inches, and the diploma itself will be 480 square inches and have a uniform border. What are the dimensions of a Furman diploma?