Worksheet: Solving Word Problems on Quadratic Equations

In this worksheet, we will practice writing simple quadratic equations from word problems then solving these equations.

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?

A40 cm, 10 cm
B10 cm, 8 cm
C40 cm, 8 cm
D40 cm, 2 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?

A24 cm, 12 cm
B12 cm, 8 cm
C24 cm, 8 cm
D24 cm, 4 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?

A7 cm, 15 cm
B15 cm, 5 cm
C7 cm, 5 cm
D7 cm, 10 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?

A24 cm, 8 cm
B8 cm, 6 cm
C24 cm, 6 cm
D24 cm, 2 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.

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.