1. If a number is added to its square, the result is 56. What is the number?
2. If a number is subtracted from its square, the result is 72. what is the number?
3. A positive number is 30 less than its square. what is the number?
4. A negative number is 42 less than its square. What is the number?
5. What two consecutive negative integers whose product is 90?
6. What two consecutive positive odd integers whose product is 143?
7. The sum of the squares of two consecutive positive even integers is 340. what are the
integers?
8. The sum of the squares of two consecutive negative even integers is 100. what are the
integers?
9. The length of a rectangle is 8 cm greater than its width. what are the dimensions if its
area is 105 cm2(squared)?
10. The length of a rectangle is 6 cm less than twice its width. If its area is 108 cm2(squared)
what are its dimensions?
11. What are the dimensions of a rectangle whose perimeter is 46 m and whose area is
126m2(squared)
12. what are the dimensions of a rectangle whose perimeter is 42 m and whose area is
104m2(squared)?
13. The sum of two different numbers is 25 and the sum of their squares is 313. what are
the numbers.
14. The difference of two positive numbers is 5 and the sum of their squares is 233.
What are the numbers?
15. Originally the dimensions of a rectangle were 20 cm by 23 cm. When both
dimensions were decreased by the same amount, the area of the rectangle
decreased by 120 cm2(squared). What are the dimensions of the new rectangle?
16. Originally a rectangle was twice as long as it was wide. When 4 m were added to
its length and 3 m subtracted from its width, the resulting rectangle had an area of
600 m2(squared). What are the dimensions of the new rectangle?
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