Quadratic word problems 1
1. A plot of land for sale has a width of x ft., and a length that is 8ft less than its width. A farmer will only purchase the land if it measures 240 square feet. What value of x will cause the farmer to purchase the land?

2. The length of a rectangle is 5 inches more than twice a number. The width is 4 inches less than the same number. If the area of the rectangle is 15, find the number

3. The square of a number exceeds the number by 72. Find the number.

4. Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second.

5. The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is 4 more than eight times the age of the oldest child. Find the ages of the three children.

6. The altitude of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find its base and altitude

7. The length of a rectangle exceeds its width by 4 inches. Find the dimensions of the rectangle if its area is 96 square inches.

8. If the measure of one side of a square is increased by 2 centimeters and the measure of the adjacent side is decreased by 2 centimeters, the area of the resulting rectangle is 32 square centimeters. Find the measure of one side of the square (the original figure).

9. Find two consecutive odd integers whose product is 99.

10. A certain number added to its square is 30. Find the number.

11. Collin is building a deck on the back of his house. He has enough lumber for the deck to be 144 square feet. The length should be 10 feet more than its width. What should the dimensions of the deck be?

12 The product of two consecutive negative odd integers is 483. Find the integers.

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