Question

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?

A. 6≤l≤8
B. 4≤l≤8
C. 4≤l≤6
D. 6≤l≤10

Answer 1

Answer: Option 'A' is correct.

Explanation:

Since we have given that

Area should not be smaller than 24 square feet

Area should not be bigger than 48 square feet

Let the width be 'w'.

Let the length be 'w+2'

So, Area of square would be

`w(w+2)=24\\\\w^2+2w=24\\\\w^2+2w-24=0\\\\w^2+6w-4w-24=0\\\\w(w+6)-4(w+6)=0\\\\(w+6)(w-4)=0\\\\w=-6,4`

If Area = 48 then it would be

`w(w+2)=48\\\\w^2+2w-48=0\\\\w^2+8w-6w-48=0\\\\w(w+8)-6(w+8)=0\\\\(w+8)(w-6)=0\\\\w=-8,6`

So, the range for the width would be

4≤w≤6

4+2≤w+2≤6+2

6≤l≤8 i.e the range for the length .

Hence, Option 'A' is correct.

Answer 2

A. 6≤l≤8

Explanation:

According to the question,

width: x

Length: 2 + x

Part B and D are eliminated.

B) 4≤l≤8

the difference should be of 2 whereas in this the difference is of 4

D) 6≤l≤10

the difference should be of 2 whereas in this the difference is of 4

C) 4≤l≤6

If the length is 4, width will be 2 so the area will be lesser than 24. Therefore, this is incorrect.

A) 6≤l≤8

If the length is 6, width will be 4 which will make the area 24.

If the length is 7, width will be 5 which will make the area 35.

If the length is 8, width will be 6 which will make the area 48.

Therefore, all the areas with this length are within the given range.

A is the correct answer.

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