Kevin wants to buy an area rug for his living room. he would like the area rug to be no smaller that 24 square feet and no bigger than 48 square feet. if the length is 2 feet more than the width, what are the range of possible values for the length?

To solve this problem you must apply the proccedure shown below:

1- You have that the area rug must be no smaller that and no bigger than and its length is more than its width.

2- The area of a rectangle can be calculated by multiplying the width by the length, if the length is more than the width, you have that:

Where is the area, is the width and is the length.

3- Based on the information above, you can express it as below:

4- You can separate to solve it if you want to see it better:

5- Then, you have the following result:

6- And the length is:

Therefore, the answer is:

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15