SOLUTION: An open box with a square base stands 6 inches tall. The total surface area of the outside of the box is 640 square inches. What are the dimensions of the base?

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: An open box with a square base stands 6 inches tall. The total surface area of the outside of the box is 640 square inches. What are the dimensions of the base?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 526345: An open box with a square base stands 6 inches tall. The total surface area of the outside of the box is 640 square inches. What are the dimensions of the base?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The surface area of this open box consists of the area of the four sides of the box plus the area of the base of the box. If the base is x by x inches, then each side has an area of 6x square inches and the base hase has an area of x%5E2 square inches, so the total surface area of the open box (no top) is:
SA+=+4%286x%29%2Bx%5E2 and this is said to equal 640 square inches, so...
x%5E2%2B24x+=+640 Add 640 to both sides.
x%5E2%2B24x-640+=+0 Solve by factoring or the quadratic formula.
%28x%2B40%29%28x-16%29+=+0 Apply the zero product rule.
x%2B40+=+0 or x-16+-+0 therefore:
x+=+-40 or x+=+16 Discard the negative solution as the dimensions of the base must be positive.
x+=+16
The dimensions of the base are 16 inches by 16 inches.