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 .

34

step-by-step explanation:

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -