Answer:
Length = 15 miles and width = 8 miles.
Step-by-step explanation:
Given : A rectangle whose width is 7 miles less than it’s length and whose area is 120 square miles.
To find : Find the dimensions of a rectangle .
Solution : We have given length and width of a rectangle .
According to question :
Let us consider the length of a rectangle = x .
Width is 7 miles less than length
Width = x -7.
Area of rectangle = length * width
Plugging the values of length ,width and area.
Area of rectangle = length * width
120 = x * (x-7)
120 = x² - 7x
On subtracting 120 from both sides and switching sides.
x² - 7x - 120 =0.
On factoring
x² - 15x +8x - 120 =0.
Taking common x from two terms and 8 from last two terms.
x (x -15) + 8( x- 15) = 0
On grouping
(x +8) (x -15) = 0
x +8 = 0 and x-15= 0
x = -8 and x = 15.
So length can not be negative values
Then x = 15 miles.
now, width = 15 -7 = 8 miles.
Therefore , Length = 15 miles and width = 8 miles .
