Question

Please help me....trying to get my HS diploma, i did not graduate :(

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 bigger than 80 square feet. If the length is 2 feet more than the width, what are the range of possible values for the length?

Answer 1

`area = l * w \\ but \: w = l - 2`

`area = l(l - 2) = l {}^(2) - 2l`

`l {}^(2) - 2l \geqslant 48 \\ l {}^(2) - 2l - 48 \geqslant 0 \\ (l + 6)(l - 8) \geqslant 0`

`l {}^(2) - 2l \leqslant 80 \\ l {}^(2) - 2l - 80 \leqslant 0 \\ (l + 8)(l - 10) \leqslant 0`

Sol 1: L in ]-∞,-6]U[8,∞[

Sol 2: L in [-8,10]

Intersection:

L belongs [-8,-6[U[8,10]

But Length cannot be negative

L belongs [8,10] or 8≤L≤10

Answer 2

It would be B.

Explanation: