Marla is hanging a banner diagonally across a rectangular room. The length of the room is 2 feet shorter than its width. If the total area of the room is 120 square feet, what is the length of the banner (in feet)? Choose the correct choice from the following options: A) Between 13 and 14 B) Between 14 and 15 C) Between 15 and 16 D) Between 16 and 17 E) Between 17 and 18
To solve this, we first need to set up an equation for the area of the room. If x is the width, then we have   x(x - 2) = 120. By putting the equation in standard form, we get x^2-2x-120=0. By using the quadratic formula, we get roots of -10 and 12. We know that x is the width, and x-2 is the length, so by using the roots, we get 12 as the width (x), and 10 as the length (x-2).   Once we have this, we can use the Pythagorean Theorem to solve for the diagonal. Plugging in the length and width, we will get d^2=12^2+10^2   =144+100= 
<gadget id="calculator">144+100</gadget>
<output>244</output>
244   The square root of 244 is less than 16, since 16^2= 256. Going down a number, we can compute 15^2 = 225 &lt; 224. Therefore, the length of the diagonal must be between 15 and 16.   The correct answer is Between 15 and 16.
<result>C</result>
Marla is hanging a banner diagonally across a rectangular room. The length of the room is 2 feet shorter than its width. If the total area of the room is 120 square feet, what is the length of the banner (in feet)?