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Mama L [17]
3 years ago
6

Kevin wants to buy an area rug for his living room. He would like the area rug to be no smaller that 48 square feet and no bigge

r than 80 square feet. If the length is 2 feet more than the width, what are the range of possible values for the length?
Mathematics
1 answer:
mariarad [96]3 years ago
3 0

Answer:

8-10 feet

Step-by-step explanation:

If the length of the carpet is two more than the width, the width can be expressed as x and the length can be expressed as x+2. This means that the area(x^2+2x) must be greater than 48 but no less than 80.

Now we can solve for both the maximum and minimum cases:

x^2+2x=48, x^2+2x-48=0, now we can factor, (x+8)(x-6)=0, and now we can use the Zero Product Property to find x=-8;x=6. Since we cant have negative width, x at least has to be equal to 6.

x^2+2x=80,x^2+2x-80=0, now we can factor, (x+10)(x-8), and now using the Zero Product Property to find x=-10;x=8, and since it must be positive, at most x can equal 8.

Now since the length is two more than the width, x, you add two to both of these values and get a range of 8-10 feet.

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