MPM 2D1
QUADRATIC EQUATION WORD PROBLEMS
NAME:
Complete 6 of the following problems. You must include two number problems, two geometry problems,
and two of the border problems. Show all your work and draw diagrams where possible.
Number Problems
1. The sum of two positive numbers is 12. If their product is 35, find the numbers.
2. The sum of the squares of 2 positive consecutive odd numbers is 130. Find the numbers.
3. The difference between two numbers is 4. If their product is 45, find the numbers.
4. The sum of the squares of 2 consecutive even positive numbers is 452. Find the numbers.
5. The sum of the squares of three consecutive positive integers is 194. Find the integers.
6. The product of two consecutive even integers is 288. What are the integers?
7. The sum of a number and its square is 272. Find the number.
8. A bunch of your friends are at your house one night and you decide to order a pizza. The pizza costs
$22.50. Just before it is delivered one person has to leave. This means that the remaining people
must pay an extra $.75 each. Find the original number of people at your house.
Geometry Problems
9. The hypotenuse of a right angled triangle is 15 cm. The sum of the other two sides is 21 cm. Find the
lengths of the other two sides.
10. The height of a triangle is 2 m more than the base. The area of the triangle is 17.5 m 2. Find the length
of the base and the height of the triangle.
11. The length of a rectangle is 5 cm more than twice the width. The area of the rectangle is 33 cm2. Find
the dimensions of the rectangle.
12. The area of a rectangular field is 2275 m2. The field is enclosed by 200 m of fence. What are the
dimensions of the field?
13. The diagonal of a rectangle is 8 cm. the length of the rectangle is 1.6 m more than the width. Find the
dimensions of the rectangle.
Border Problems
14. A rectangular playground 40 m by 60 m is to be doubled in area by extending the length and width by
an equal amount. By how much should the length and the width be lengthened?
15. A rectangular skating rink is 30 m by 20 m. It is to be doubled in area by adding a strip at one end and
a strip of equal width along one side. Find the width of the strip.
16. You have a picture 8” by 10” and you want to matt and frame it. The area of the matt must equal the
area of the picture. Find the width of the matt correct to one decimal place.
17. A rectangular building 100 m by 80 m is surrounded by a lawn of uniform width. The area of the lawn
equals the area of the building. Find the width of the lawn. (Answer correct to one decimal)
18. A rectangular sheet of metal 20 cm by 40 cm is made into a lidless box by cutting squares of equal size
from the corners of the sheet and then folding up the sides to form a box. The bottom of the box has
an area of 300 cm2. Find:
a) the length of each square that was cut out of the sheet.
b) the dimensions of the base of the box
c) the volume of the box
Answers:
1. x2 -12x + 35 = 0 ; 5 & 7
2. x2 + 2x – 63 = 0 ; 7 & 9
3. x2 + 4x – 45 = 0 ;
5&9
4. x2 + 2x – 224 = 0 ; 14 & 16
5. x2 + 2x - 63 = 0 ; 7, 8, 9
6. x2 + 2x -288 = 0 ;
16 & 18
7. x2 + x – 272 = 0 ;
16 & -17
8. x2 – x + 30 = 0 ; 6
9. x2 – 21x + 108 = 0 ; 9 & 12
10. x2 + 2x – 35 = 0 ;
5&7
11. 2x2 + 5x -33 = 0 ;
3 & 11
12. x2 – 100x + 2275 = 0 ; 35 & 65
13. x2 +1.6x – 30.72 = 0 ;
4.8
14. x2 + 100x – 2400 = 0 ; 20
15. x2 + 50x – 600 = 0 ; 10
16. x2 + 9x – 20 = 0 ;
1.84
17. x2 + 9x – 200 = 0 ; 18.4
18. a) x2 – 30x + 125 = 0 ; 5
b) 10 cm by 30 cm
c) 1500 cm3