Worksheet: Using Quadratic Equations to Solve Word Problems

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?

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.

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.