One rectangular-shaped piece of metal sliding needs to be cut to cover the exterior of a pole barn. The area of the piece is 30 ft^2. The length is 1 less than 3 times the width. How wide should the metal piece be? Round to the nearest hundredth of a foot.
A. 3.33 ft
B. 4.3 ft
C. 1 ft
D. 30 ft

Question

One rectangular-shaped piece of metal sliding needs to be cut to cover the exterior of a pole barn. The area of the piece is 30 ft^2. The length is 1 less than 3 times the width. How wide should the metal piece be? Round to the nearest hundredth of a foot.
A. 3.33 ft
B. 4.3 ft
C. 1 ft
D. 30 ft

radar · Answer

Let w = width then
3w -1 = length (given)
Area =30 sq ft  (given)
Area = length times width
(3w-1)*(w) = 30    given.  Clear the parenthesis
3w^2 -w = 30   Subtract 30 from both sides.
3w^2 -w -30 = 0      Factor the quadratic
(3w - 10)(w + 3) = 0    Solve using algebra
w + 3 = 0 , then w = -3    Discard as dimension can't be negative
3w - 10 = 0
w=10/3 or 3 1/3 or 3.33
length equal 10 - 1 = 9