A rectangle is 6 km longer than it is wide. Find the dimensions of the rectangle if its area is 112 sq-km.

Length=
Width=

Solving Polynomial Equations by Factoring

Question

A rectangle is 6 km longer than it is wide. Find the dimensions of the rectangle if its area is 112 sq-km.

Length=
Width=

Solving Polynomial Equations by Factoring

sburchette · Answer

Have you constructed your equations or assigned variables yet?

anonymous · Answer

no

sburchette · Answer

What if we let x = length. That would make the width = x-6 since the length is 6 km longer than the width. 

Since area is length * width, we have that x(x-6) = 112. Can you solve the equation from there?

anonymous · Answer

no

sburchette · Answer

We need to have the equation in factored form with zero on one side. If we distribute x on the left side, we get $$x^2-6x=112$$ We can subtract 112 from both sides to obtain $$x^2-6x-112=0$$The left side factors into $$(x+8)(x-14)=0$$ The solutions for x are -8 and 14. Since length cannot be negative, x must be 14. Since the width is 6 less than the length, the width is 8.