area of two rectangles: the length is 3 times its width....

[sweetroca888]

The length of a rectangle is 3 times its width. If the width were increased by 4 and the length remained the same, the resulting rectangle would have an area of 231 square inches. Find the dimensions of the original rectangle.

 

[stapel]

What have you tried? How far have you gotten?

Please reply showing your work and reasoning so far, starting with a description of the picture you drew and the definition you gave to the variable you picked. Thank you.

Eliz.

 

[sweetroca888]

work done

I think to find the width of the larger rectangle it would be 3w(w+4)=231
right? But I am not sure, so I am afraid to further. Or maybe it would be
3w(w)=231 and then the smaller rectangle would be 3w(w-4)=A, I'm so
confused.

 

[stapel]

I think to find the width of the larger rectangle it would be 3w(w+4)=231

Are you saying that the width is "3w(w+4)=231"? Or did you mean the following...?

"I picked w to stand for the original width, so then 3w was the original length. For the new rectangle, the width will be w + 4, but the length will still be 3w. The area then is 3w(w + 4) = 231."

If so, then your reasoning was correct. Now solve the quadratic equation for the original width, and back-solve for the length.

Eliz.