John is building a rectangular fence around a garden. The length will be 5 feet shorter than its width. If the total area of the garden is 176 square feet, what is the length of the diagonal (in feet)?	Choose the correct choice from the following.
A) Between 18 and 19
B) Between 19 and 20
C) Between 20 and 21
D) Between 21 and 22
E) Between 22 and 23
To solve this, we first need to set up an equation for the area of the garden. If x is the width, then we have   x(x - 5) = 176. By putting the equation in standard form, we get x^2-5x-176=0. By using the quadratic formula, we get roots of -11 and 16. We know that x is the width, and x-5 is the length, so by using the roots, we get 16 as the width (x), and 11 as the length (x-5).   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=16^2+11^2   =256+121= 
<gadget id="calculator">256+121</gadget>
<output>377</output>
377   The square root of 377 is less than 20, since 20^2= 400. Going down a number, we can compute 19^2 = 361 &lt; 377. Therefore, the length of the diagonal must be between 19 and 20.   The correct answer is Between 19 and 20.
<result>B</result>
John is building a rectangular fence around a garden. The length will be 5 feet shorter than its width. If the total area of the garden is 176 square feet, what is the length of the diagonal (in feet)?