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Worksheet: Using Quadratic Equations to Solve Word Problems

Q1:

The length of a rectangle is 2 cm more than its width. If its area is 80 cm2, what are its length and width?

  • A 40 cm, 8 cm
  • B 40 cm, 2 cm
  • C 40 cm, 10 cm
  • D 10 cm, 8 cm

Q2:

The length of a rectangle is 4 cm more than its width. If its area is 96 cm2, what are its length and width?

  • A 24 cm, 8 cm
  • B 24 cm, 4 cm
  • C 24 cm, 12 cm
  • D 12 cm, 8 cm

Q3:

The length of a rectangle is 10 cm more than its width. If its area is 75 cm2, what are its length and width?

  • A 7 cm, 5 cm
  • B 7 cm, 10 cm
  • C 7 cm, 15 cm
  • D 15 cm, 5 cm

Q4:

The length of a rectangle is 2 cm more than its width. If its area is 48 cm2, what are its length and width?

  • A 24 cm, 6 cm
  • B 24 cm, 2 cm
  • C 24 cm, 8 cm
  • D 8 cm, 6 cm

Q5:

The length of a rectangle is 26 cm more than its width. Given that its area is 120 cm2, determine its perimeter.

Q6:

The length of a rectangle is 15 cm more than its width. Given that its area is 54 cm2, determine its perimeter.

Q7:

The length of a rectangle is 10 cm more than its width. Given that its area is 24 cm2, determine its perimeter.

Q8:

The side length of a square is cm, and the dimensions of a rectangle are cm and 2 cm. Given that the sum of their areas is 8 cm2, determine the perimeter of the square.

Q9:

The side length of a square is cm, and the dimensions of a rectangle are cm and 5 cm. Given that the sum of their areas is 14 cm2, determine the perimeter of the square.

Q10:

The side length of a square is cm, and the dimensions of a rectangle are cm and 8 cm. Given that the sum of their areas is 9 cm2, determine the perimeter of the square.

Q11:

The length of a rectangle is 3 cm more than double the width. The area of the rectangle is 27 cm2. Write an equation that can be used to find , the width of the rectangle, in centimeters.

  • A
  • B
  • C
  • D
  • E

Q12:

A rectangular photograph measuring 6 cm by 4 cm is to be displayed in a card mount in a rectangular frame, as shown in the diagram.

Write an equation that can be used to find , the width of the mount, if its area is 64 cm2.

  • A
  • B
  • C
  • D
  • E