Question

The perimeter of rectangle is twice the sum of its length and its width.the perimeter is 22 meters and its length is 2 meters more than twice its width. What is its length?

Answer 1

P=2(l+w)
P= perimeter= 22m
l=length= (2w+2)
w=width

Step 1:
Solve for w
substitute l=(2w+2) in equation

22=2[(2w+2)+w]
combine like terms inside parentheses

22=2(3w+2)
use distributive property to multiply 2 by everything inside parentheses

22=(2*3w) + (2*2)
22=6w+4
subtract 4 from both sides
18=6w
divide both sides by 6
3 meters=w= width

Step 2:
Solve for length by substituting w=3

22=2(l+w)
22=2(l+3)
22=(2*l) + (2*3)
22=2l+6
16=2l
8 meters = l= length

Check:
22=2(l+w)
22=2(8+3)
22=2(11)
22=22

Hope this helps! :)

Answer 2

P = 2(L + W)
P = 22
L = 2W + 2

22 = 2(2W + 2 + W)
22 = 2(3W + 2)
22 = 6W + 4
22 - 4 = 6W
18 = 6W
18/6 = W
3 = W.....this is the width

L = 2W + 2
L = 2(3) + 2
L = 6 + 2
L = 8 meters <=== this is the length