Question

The perimeter of a rectangle is 62 m. The length is four more than two times the width. What is the length?

Answer 1

We can translate these sentences into equations:

"The perimeter of a rectangle is 62 m"
$\sf P=2l+2w$
$\sf 62=2l+2w$

"The length is four more than two times the width."
$\sf l=2w+4$

Now we can plug in what 'l' equals in the 2nd equation into the first equation:

$\sf 62=2l+2w$

$\sf 62=2(2w+4)+2w$

Distribute:

$\sf 62=4w+8+2w$

Combine like terms:

$\sf 62=6w+8$

Subtract 8 to both sides:

$\sf 54=6w$

Divide 6 to both sides:

$\sf w=9$

So this is our width, we can plug this into any of the two equations to find the length:

$\sf l=2w+4$

$\sf l=2(9)+4$

Multiply:

$\sf l=18+4$

Add:

$\boxed{\sf l=22~m}$

Answer 2

--------------------------------------------------
Define length and width
--------------------------------------------------
Let x be the width
width = x
Length = 2x + 4

--------------------------------------------------
Formula
--------------------------------------------------
Perimeter = 2(length + width)

--------------------------------------------------
Find Length and width
--------------------------------------------------
62 = 2(2x + 4 + x)
62 = 2(3x + 4)             ← combine like terms   
62 = 6x + 8                 ← remove bracket   
62 - 8 = 6x                  ← minus 8 on both sides 
6x = 54                       ← swap sides  
x = 54 ÷ 6                   ← divide by 6 on both sides
x = 9 m

--------------------------------------------------
Find Length and Width
--------------------------------------------------
Width = x = 9 m
Length = 2x + 4 = 2(9) + 4 = 22 m

--------------------------------------------------
Answer: Length = 22m
--------------------------------------------------