Applications of Quadratic Equations Word Problems

If the area of the shaded region in the diagram shown is 103 square feet, solve for x and find the dimensions of the inside rectangle.

x =​ (a)   ​ (b)  

Dimensions of inside rectangle:

Short side = ​ (c)   feet

Long side = ​ (d)   feet

• 5
• feet
• 4
• 10
• 11
• square feet
• 13
• inches
• 6
• 8

Answer explanation

The side length of a square can be expressed as 2x + 3.

If the area of the square is 121 square meters, what is the value of x?

x = (a)   ​​ (b)  

• 4
• 5
• 6

• 7

• 8

• mm
• cm
• m
• km

Answer explanation

The product of two positive consecutive integers is 132.

Find both of the integers.

• 10 and 11

• 11 and 12

• 12 and 13

• 13 and 14

• 31 and 32

Answer explanation

Find two positive even consecutive integers such that the square of the smaller integer is 10 more than the larger integer.

• 4 and 6

• 6 and 8

• 8 and 10

• 10 and 12

• 2 and 4

Answer explanation

Find three positive consecutive integers such that the product of the first and the third integer is 17 more than 3 times the second integer.

• 1, 2, 3

• 2, 3, 4

• 3, 4, 5

• 4, 5, 6

• 5, 6, 7

Answer explanation

• 10.95
• 8.82
• 21.21
• seconds
• feet
• minutes
• 8.84
• 35.13

Answer explanation

• 5
• 4
• 6
• 3
• seconds
• 2
• minutes
• feet
• feet/second

Answer explanation

• seconds
• 169.39
• feet
• feet/second
• yards
• minutes
• 3.16
• 16.83
• 95

Answer explanation

• Yes

• No
• 12.25
• feet
• inches
• 10
• seconds
• 0.625
• 1.5
• 14.6

Answer explanation

• 10.48
• seconds
• 2.22
• 0.20
• 0.18
• 12.70
• minutes
• meters
• centimeters

Answer explanation