Respuesta :
Answer:
Approximately 3.5 feet - Option B
Step-by-step explanation:
Imagine that you have this walkway around the garden, with dimensions 30 by 20 feet. This walkway has a difference of x feet between it's length, and say the dimension 30 feet. In fact it has a difference of x along both dimensions - on either ends. Therefore, the increases length and width should be 30 + 2x, and 20 + 2x, which is with respect to an increases area of 1,000 square feet.
( 30 + 2x ) [tex]*[/tex] ( 20 + 2x ) = 1000 - Expand "( 30 + 2x ) [tex]*[/tex] ( 20 + 2x )"
600 + 100x + 4[tex]x^2[/tex] = 1000 - Subtract 1000 on either side, making on side = 0
4[tex]x^2[/tex] + 100x - 400 = 0 - Take the "quadratic equation formula"
( Quadratic Equation is as follows ) - [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex],
[tex]x=\frac{-100+\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad \frac{5\left(\sqrt{41}-5\right)}{2}[/tex],
[tex]x=\frac{-100-\sqrt{100^2-4\cdot \:4\left(-400\right)}}{2\cdot \:4}:\quad -\frac{5\left(5+\sqrt{41}\right)}{2}[/tex]
There can't be a negative width of the walkway, hence our solution should be ( in exact terms ) [tex]\frac{5\left(\sqrt{41}-5\right)}{2}[/tex]. The approximated value however is 3.5081...or approximately 3.5 feet.
