Find the dimensions of a rectangle whose width is 7 miles less than it's length and whose area is 120 square miles.

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.

The width is 8 and the length is 15. 15x8=120 15-8=7