SOLUTION: A rectangle has a perimeter of 14 feet, and twice its length l is equal to two more than 4 times its width w. Find l and w.

Question 251162: A rectangle has a perimeter of 14 feet, and twice its length l is equal to two more than 4 times its width w. Find l and w.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Define your variables and list known items:
p = perimeter = 14
l = length
w = width
p = 2l + 2w = 2(l+w)
l = 4w + 2
.
substituting l = 4w+2 into the perimeter equation
14 = 2(4w+2) + 2w
.
multiply to remove the parentheses
14 = 8w +4 + 2w
.
collect terms
14 = 10w +4
.
subtract 4 from both sides
10 = 10w
.
divide both sides by 10
1 = w
w = 1
.
substituting back into l = 4w+2
l = 4(1) + 2 = 6
.
checking the perimeter
2l = 12
2w = 2
2l + 2w = 14, which is correct.
.
so our answer is:
l=4
w=1
.
done
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