The length of a rectangle is 3 times its width. If the length were increased by 2 inches and the width by 1 inch, the new perimeter would be 62 inches. What is the width and length of the rectangle?

If w represents the width of the rectangle, then which equation could be used to solve for w?

(w + 1)(3w + 2)=62
2(4w + 3) = 62
2(3w + 3) = 62

Question

The length of a rectangle is 3 times its width. If the length were increased by 2 inches and the width by 1 inch, the new perimeter would be 62 inches. What is the width and length of the rectangle?

If w represents the width of the rectangle, then which equation could be used to solve for w?


(w + 1)(3w + 2)=62
2(4w + 3) = 62
2(3w + 3) = 62

mathmate · Answer

1. Given
The length of a rectangle is 3 times its width  
 If the length were increased by 2 inches and the width by 1 inch,  the new perimeter would be 62 inches.

2. Unknowns L=length, W=width

3. Equation:
L=3W
Perimeter = 2(L+2+ W+1)=62
Put in L=3W to eliminate L
2(3W+2+W+1)=62

4. Solve to find W
5. Solution : interpret results

Steps 4 and 5 are not necessary.  From step 3, can you find the right choice?