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

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?

A. (w + 1)(3w + 2) = 62

B. 2(4w + 3) = 62

C. 2(3w + 3) = 62

Answer 1

Length is 3 time width:  L = 3W

 

Perimeter is L+L+W+W

 

That would mean 3W+3W+W+W = 9W would be the perimeter of the original rectangle

 

Increase the length by 2 and width by 1 would give you L=3W so 3W + 1 and W=W so W+2

 

Add those together and you would have 3W + 2 + 3W + 2 + w +1 + w + 1 = 8W + 6 (Simplified: 2(4W+3))

 

This would add up your four sides (3W + 2 is the length, w + 1 is the width)

 

Answer B.