The width of a rectangle is 3 inches less than the length. The perimeter is 58 inches. Find the length and the width.

Question

 The width of a rectangle is 3 inches less than the length. The perimeter is  58 inches. Find the length and the width.

Answer 1

Let

w = width of Rectangle

L = length of Rectangle

 

w = L - 3   (Width is 3 inch less than length)

 

2w + 2L = 58  (perimeter is 58)

 

Substitute w above

 

2(L -3 ) + 2L = 58

 

2L - 6 + 2L = 58

4L = 64

L = 16

W = 16 - 3 = 13

 

Length = 16

Width = 13

 

Answer 2

Well we know that the total perimeter is 58 and that two of the sides will be three less than the other two sides.

If  the perimeter was 60 all the sides would be equal and would be 15 but that is not the case but it does give us an idea of what the numbers could be. If two sides were 15 the other two would be 14, so knowing this we can just use the ratio by increasing the sides until we have two sides that are 3 inches more than the other two.  So if we increase the longer sides by one inch we would have to decrease the smaller sides by 1 inch as well.

 

15:14
16:13
17:12
18:11

 

So we can see the sides that fit are problem are 16:13 because the smaller sides are 3 inches less then the other two sides.  So length = 16 and width = 13