Question

Two less than three times the width of a rectangle is equal to the length. The area of the rectangle is 65 square ft. What is the length of the rectangle?

Answer 1

the length of this beautiful, significant shape is 2.

Answer 2

Length of the rectangle = 13 ft

Explanation:

Let l be the length and w be the width of this rectangle.

Two less than three times the width of a rectangle is equal to the length, that is

3w - 2 = l---------------------------eqn 1

The area of the rectangle is 65 square ft

l x w = 65

Substituting eqn 1

(3w - 2) x w = 65

3w² - 2w -65 = 0

Solving quadratic eqn

`w=(-(-2)\pm √((-2)^2-4* 3* (-65)))/(2* 3)=(2\pm √(4+780))/(6)\\\\w=(2\pm √(784))/(6)\\\\w=(2\pm 28)/(6)\\\\w=(2+28)/(6)\texttt{ or }w=(2-28)/(6)\\\\w=5\texttt{ or }w=-4`

w cannot be negative

Hence width, w = 5 ft

Substituting in eqn 1

3 x 5 - 2 = l

l = 13 ft

Length = 13 ft

Length of the rectangle = 13 ft