Respuesta :
Let's call the width [tex] x [/tex]. Since the length is three more than the width, it is [tex] x+3 [/tex].
The area (which we know to be 70) is given by the multiplication of width and length:
[tex] x(x+3) = 70 \iff x^2+3x = 70 \iff x^2+3x-70 = 0 [/tex]
To solve this equation, you can use the usual quadratic formula: given an equation [tex] ax^2+bx+c=0 [/tex], the two solutions are
[tex] x_{1,2} = \frac{-b\pm\sqrt{b^2-4ac}}{2a} [/tex]
which in your case becomes
[tex] x_{1,2} = \frac{-3\pm\sqrt{9+280}}{2} = \frac{-3\pm 17}{2}[/tex]
So, two solutions are
[tex] \frac{-3-17}{20} = -10,\qquad \frac{-3+17}{2} = 7 [/tex]
Since we can't accept a negative length, we only accept the second solution.
So, the dimensions are 7 and 10
