Question

the area of a rectangle is text square and the length of the rectangle is 3 ft more than twice the width. find the dimensions of the rectangle length and width

Answer 1

Area of rectangle = 35 feet square
Let the Width of rectangle is x feet.
Length of rectangle is 3 feet more than twice the width.
Thus,Length can be written as: 2x + 3

Area of rectangle is product of its length and width.
So,

Area = Length x Width

$35 = x (2x + 3) \\ \\ 35 = 2 x^{2} +3x \\ \\ 2 x^{2} + 3x - 35 = 0 \\ \\ 2 x^{2} + 10x - 7x - 35 =0 \\ \\ 2x (x + 5) - 7 (x+5) = 0 \\ \\ (2x-7)(x+5)=0$

Thus
x = -5
or
x =7/2 = 3.5

Since the measure of width cannot be negative, we neglect x = -5. and keep the value x = 3.5

Therefore,
Width = 3.5 feet
Length = 2x + 3 = 2(3.5) + 3 = 10 feet