Quadratic equations

Question

The question is written like this:

 

The width of a rectangle is (x+2) cm. The perimeter of the rectangle is 6(x+1) cm. The area of the rectangle is 18 cm². Show that 2x²+5x-16=0.

 

What is the working out to solve this question? We had hints in maths class but they weren’t very useful. 

 

Thanks!

Answer 1

w = x + 2

Let l = the length

P = 2l + 2w

6(x + 1) = 2(x + 2) + 2l

6x + 6 = 2x + 4 + 2l

4x + 2 = 2l

2x + 1 = l

 

A = lw

18 = (2x + 1)(x + 2)

18 = 2x² + 4x + x + 4

18 = 2x² + 5x + 4

0 = 2x² + 5x - 16