Answer:
5.69 feet by 19.69 feet
Step-by-step explanation:
Given : A gardener wants to create a rectangular vegetable garden in a backyard. He wants it to have a total area of 112 square feet, and it should be 14 feet longer than it is wide.
Let x be the breadth of the rectangular vegetable garden
So, length of the rectangular vegetable garden = ( x + 14 ) feet
To find: dimensions that a gardener should use for the vegetable garden
Solution :
We know that area of the rectangle is equal to length ( l ) × breadth ( b )
Area of the rectangular garden = 112 square feet
According to question,
[tex]x(x+14)=112\Rightarrow x^2+14x-112=0[/tex]
In order to find roots, use quadratic formula which states that for equation [tex]ax^2+bx+c=0[/tex], roots are [tex]\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Therefore, for equation [tex]x^2+14x-112=0[/tex], roots are [tex]\frac{-14\pm \sqrt{196+448}}{2}=\frac{-14\pm \sqrt{644}}{2}[/tex]
Being a dimension, breadth can not be negative, so x = [tex]\frac{-14- \sqrt{644}}{2}[/tex] is rejected
Therefore,
[tex]x=\frac{-14+ \sqrt{644}}{2}=5.69\Rightarrow l = x+14=5.69+14=19.69[/tex]
So, length = 19.69 feet and breadth = 5.69 feet
