Marla is hanging a banner diagonally across a rectangular room. The length of the room is 3 feet shorter than its width. If the total area of the room is 130 square feet, what is the length of the banner (in feet)?  Choose the correct choice.
A) between 16 and 17
B) between 17 and 18
C) between 18 and 19
D) between 19 and 20
E) between 20 and 21
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 - 3) = 130. By putting the equation in standard form, we get x^2-3x-130=0. By using the quadratic formula, we get roots of -10 and 13. We know that x is the width, and x-3 is the length, so by using the roots, we get 13 as the width (x), and 10 as the length (x-3).   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=13^2+10^2   =169+100= 
<gadget id="calculator">169+100</gadget>
<output>269</output>
269   The square root of 269 is less than 17, since 17^2= 289. Going down a number, we can compute 16^2 = 256 &lt; 269. Therefore, the length of the diagonal must be between 16 and 17.   The correct answer is between 16 and 17.
<result>A</result>
Marla is hanging a banner diagonally across a rectangular room. The length of the room is 3 feet shorter than its width. If the total area of the room is 130 square feet, what is the length of the banner (in feet)?