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 answer is a

step-by-step explanation:

step-by-step explanation:

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