Answer:
Step-by-step explanation:
Be the sides x[tex]x, x+6[/tex] you know [tex]x(x+6) = 112[/tex] or [tex]x^2 +6x -112 = 0[/tex][tex]x= -3 \pm \sqrt{9+112} = -3\pm 11[/tex] the solution is [tex]x=8, x=-14[/tex] The negative answer is to be discarded, your rectangle has sides 8 and [tex]8+6=14[/tex] miles
The length of the rectangle is 14 miles and the width of the rectangle is 8 miles.
For a rectangle with length and width L and W units, we get:
Area of the rectangle = (L × W) unit^2
Perimeter of the rectangle = 2(L + W) units
Let the width of the rectangle be represented by W, while the length is represented by L.
Given the width is 6 miles less than its length, therefore, the width can be written as,
W = (L - 6) miles
Now given the area of the rectangle is 112 sq. miles, therefore, the area of the rectangle can be written as,
Area of the rectangle = Length × Width
112 = L × W
112 = L × (L-6)
112 = L²-6L
L = 14, -8
Since the length, L can not be negative, the value of L is 14 miles, therefore, the width will be 8 miles.
Hence, the length of the rectangle is 14 miles and the width of the rectangle is 8 miles.
Learn more about Area of rectangle:
https://brainly.com/question/20693059
#SPJ2
