Quadratic functions long question 2?

Question

The length of a rectangle is five less than three times its width. Find the dimensions of the rectangle if its area is 782m^2. 

Answer 1

Let width of rectangle = x m

Then it's length = 3x - 5

Area of rectangle  x(3x - 5) = 782 m²

3x² - 5x = 782

3x² - 5x -  782 = 0

Solve the above equation by factorization.

3x² - 51x + 46x -  782 = 0

3x(x - 17) + 46(x - 17) = 0

(x - 17) (3x + 46) = 0

x - 17 = 0 and 3x + 46 = 0

x = 17 and 3x = - 46

x = 17 and x = -46/3

Length of rectangle is always positive.

So consider x = 17.

Now 3x - 5 = 3(17) - 5 = 46

Dimensions of rectangle are 51m and 46m.