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)?  Select:
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

Rationale: 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 - 3 x - 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 = 269 the square root of 269 is less than 17 , since 17 ^ 2 = 289 . going down a number , we can compute 16 ^ 2 = 256 < 269 . therefore , the length of the diagonal must be between 16 and 17 . the correct answer is a .
Answer: A