the area of a rectangular wall of a barn is 160 square feet. its length is 4 feet longer than twice its width. find the length and width of the wall of the barn

Question

The area of a rectangular wall of a barn is 160 square feet. Its length is 4 feet longer than twice its width. Find the length and width of the wall of the barn

Answer 1

L=Length W=width

LW=160 L=4+2W With two equations two unknown variables, you can solve the system of equations by substitution. Substitute 4+2W for L in the LW=160 equation to get (4+2W)W=160 or 4W+2W²=160

Rewrite that putting all terms on the left and zero on the right to get 2W² +4W -160 = 0

Divide by 2 to get W² + 2W -80 = 0 Now either factor, complete the square or use the quadratic formula

80 = 8 x 10 and 10-8=2 so W+10 and W-8 are factors

(W+10)(W-8)=0 W=-10 and W=8. Since negative lengths make no sense, Width =8 feet

Length is 4 plus 2W or 4+16 =20

L=20 feet, W= 8 feet, so Area is LW=160 If you mean a wall with area of 160 square feet, maybe that really means height and length?