a rectangle has a perimeter of 30 in. its length is one less than three times its width . what are the lengths and widths of the rectangle

Question

I am having trouble answering this question , I have read it multiple times 

Answer 1

The perimeter of a rectangle is the sum of twice its width and twice its length.

 

Let the width = x

Let the length = 3x - 1

 

Using these variables, we can write an equation that represents the perimeter.

 

2x + 2(3x -1) = 30

 

Solve the equation for x.  This will give you the width.  Once you have your x value, you will substitute it into the other expression to find the length.

Answer 2

1.  2l+2w=30

2.  l=3w-1

 

put 2. into 1. for l=

 

2(3w-1)+2w=30

8w=32

w=4

 

sub this back into l=3w-1 and solve for l

 

l=3w-1=3(4)-1 = 12-1 = 11

 

Now check does 2w+2l=30  2(4)+2(11)=8+22=30   YES !!!

 

Check w=(31/6) and l=(29/2)   does 2l+2w=30 ?    

 

Answer 3

The perimeter of a rectangle is 2(L+W),

where L is length and W is width.

 

L = 3W -1   From the 2nd sentence

2(L+W) = 30

 

Substitute the expression for L into the 2nd equation

 

2(3W-1+W)=30

6W - 2 + 2W = 30

8W = 32

W = 4

 

Using this value of W in the first equation

L = 3(4) -1 = 11