The perimeter of a rectangle is 84ft. The length is 6ft less than twice the width. What are the dimensions?

Question

 how do you properly set up this question... and how do you properly answer it..

Answer 1

Hi Amanda,

 

The perimeter of the rectangle is the sum of all its sides. Two  length = 2x and two width = 2w.

 

2x + 2y = 84

x + y = 42

 

y = 2x - 6   length is 6 less than twice the width. Plug this into the first equation

 

x + 2x - 6 = 42

3x = 48 

x = 16, and since y = 2x - 6 = 2*16 - 6 = 26

 

 

The length is 26ft and the width is 16ft

Answer 2

the perimeter of a rectangle is the 2 lengths and 2 widths added together. The formula looks like this:

P = 2L + 2w

Here's what we know:

P = 84

L = 2w - 6 (the length is 6 less than twice the length)

 

Now that we have values to our variables, let's plug them in:

84 = 2(2w - 6) + 2w

Distribute:

84 = 4w - 12 + 2w

84 = 6w - 12

Add 12 to both sides:

96 = 6w

Divide both sides by 6:

16 = w

 

Now to solve for L:

L = 2 * 16 - 6

L = 32 - 6

L = 26

 

Check:

26 * 2 + 16 * 2 = 84

52 + 32 = 84

84 = 84

Answer 3

hi Amanda-

 

 

2L + 2W = 84

 

L = 2W - 6

 

Solve the two equations by substitution.

 

 

Let us know if you need help with that part

 

Ben