SOLUTION: The Length of a rectangle is 4 yards more than twice its width. If the area is 70 square yards, find the length and width of the rectangle.

Algebra ->  Rectangles -> SOLUTION: The Length of a rectangle is 4 yards more than twice its width. If the area is 70 square yards, find the length and width of the rectangle.      Log On


   

Question 1129448: The Length of a rectangle is 4 yards more than twice its width. If the area is 70 square yards, find the length and width of the rectangle.
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
width=x
length=2x+4
product is area, so 2x^2+4x=70
x^2+2x-35=0, dividing by 2 and moving everything to one side
(x+7)(x-5)=0, only positive root is width=5 yds
length=14 yds

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

le's the length of a rectangle be L and the width W
if the length is 4 yards more than twice its width, we have
L=2W%2B4 ....eq.1
if the area is 70 square yards, we have
L%2AW=70..........substitute L from eq.1
%282W%2B4%29%2AW=70
2W%5E2%2B4W=70...simplify
W%5E2%2B2W=35
W%5E2%2B2W-35=0....factor
W%5E2%2B7W-5W-35=0
%28W%5E2%2B7W%29-%285W%2B35%29=0
W%28W%2B7%29-5%28W%2B7%29=0
%28W+-+5%29+%28W+%2B+7%29+=+0
since we are looking for width, we need only positive solution

%28W+-+5%29+=+0=>W=5...............the width
go back to eq.1
L=2W%2B4 ....eq.1
L=2%2A5%2B4
L=14 ....the length