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Math 8 Name ________________________________________
Quadratics Word Problems Date _____________________ Section _____________
For each, define variable(s), write and solve a quadratic equation and answer
the question.
Consecutive Integers:
1. Find two consecutive integers whose product is 42.
2. Find two consecutive integers whose product is 72.
3. Find two consecutive integers whose product is 90.
4. Find two consecutive even integers if the sum of their squares is 164.
5. Find three consecutive even integers if the sum of their squares is 1208.
6. Find two consecutive odd integers such that 3 times the square if the larger is 45 more than
10 times the smaller.
7. The sum of the squares of three consecutive positive odd integers is 371. What are the
integers?
8. The sum of the squares of four consecutive negative integers is 86. Find the integers.
9. Find two consecutive positive odd integers if the sum of their squares is 514.
10. Find two consecutive odd integers if the difference between their squares is 16.
11. Find three consecutive positive even integers such that the product of the two smaller
integers is 16 more than the largest.
12. Three brothers have ages that are consecutive even integers. The product of the first and
third boys’ ages is 20 more than twice the second boys age. Find the age of each of the
three boys.
13. Find three consecutive odd integers such that the product of the first and second exceeds
the third by 8.
Rectangle Problems:
14. The length of a rectangle is two more than its width. If the area of the rectangle is 63
cm2, find the length and width.
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15. A rectangle with an area of 90 in has a width that is 9 inches less than its length. Find
the length and the width.
16. The area of a rectangle is 96 square kilometers. Its width is 4 km less than its length.
Find its dimensions.
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17. The length of a rectangle is 2 cm longer than three times the width. The area is 85 cm .
Find the dimensions.
18. The length of a rectangle is 5 cm longer than its width. The area is 24 square cm. Find
the dimensions of the rectangle.
19. The width of a rectangle is 7 inches shorter than its length. The area is 78 square inches.
Find the dimensions of the rectangle
20. The area of a square is 21 more than the perimeter. Find the length of a side of the
square.
21. The length of a rectangle is five times its width. If the length is decreased by 3 and the
width is decreased by one, a new rectangle is formed with an area of 24. Find the
dimensions of the original rectangle.
22. If one side of a square is increased by one and another is the other side is increased by
two, a rectangle is formed with an area of 2 less than twice the area of the square. Find the
length of a side of the square.
23. If one side of a square is doubled and another is decreased by 2 a rectangle is formed
with an area that is 12 more than the area of the square. Find the dimensions of each
figure.
24. The length of a rectangle is 8 and the width is 6. If each dimension is increased by the
same amount, a new rectangle is formed with an area of 72 more than the area of the
original rectangle. Find the dimensions of the new rectangle.
25. If one dimension of a square is increased by 10 and the other is increased by 6, a new
rectangle is formed with an area that is 60 more than five times the area of the square. Find
the dimensions of the square.
Triangles:
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26. The base of a triangle is 4 cm shorter than the height. The area is 30 cm . Find the base
and the height of the triangle.
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27. The height of a triangle is 8 inches less than the base. The area of the triangle is 64 in .
Find the dimensions of the triangle.
28. The larger leg of a right triangle is 7 cm more than the smaller leg. The hypotenuse is 17
cm. Find each leg.
29. The smaller leg of a right triangle is 14 cm smaller than the larger leg. The hypotenuse is
2 cm larger than the larger leg. Find each side of the triangle.
30. One leg of a right triangle is 7 cm longer than the other leg. If the hypotenuse measures
13 cm, find each leg.
More Rectangles:
31. A rectangular garden is 25 ft by 50 ft. It is increased on all sides by the same amount and
its area increases 400 sq. ft. By how much was each dimension increased?
32. A living room rug is 9 ft by 12 ft. A strip of floor of equal width is uncovered on all sides of
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the room. If the area of the uncovered floor is 270 ft , how wide is the strip?
33. A rectangular patio measures 20 meters by 12 meters. A walk of uniform width surrounds
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the patio. The total area of the patio and the walk is 560 m . How wide is the walk?
34. A rectangular picture is 7 inches by 5 inches and has a border of uniform width surrounding
it. If the area of the picture and the border is 80 square inches, find the width of the border.
35. By what like amount does the length and width of a 6” by 4” rectangle need to be
increased for its area to be doubled?
36. A rectangular painting has a length that is ten inches more than the width. The painting is
in a frame that is two inches wide all the way around. The total area of the picture and the
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frame is 336 in . What are the dimensions of the painting?
Multiple Choice:
37. A farmer has a rectangular field that measures 100 feet by 150 feet. He plans to increase
the area of the field by 20%. He will do this by increasing the length and the width by the
same amount, x. Which equation represents the area of the new field?
[A] (100+2x)(150+x) = 18,000
[B] (100+x)(150+x) = 18,000
[C] (100+x)(150+x) = 15,000
[D] 2(100+x) + 2(150+x) = 15,000
38. The length of a rectangular window is 5 feet more than its width. The area of the window is
36 square feet. Which equation can be used to find the dimensions of the window?
[A] w2 – 5w – 36 = 0
[B] w2 + 5w + 36 = 0
[C] w2 – 5w + 36 = 0
[D] w2 + 5w – 36 = 0
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