SOLUTION: Rosita's Christmas present from Calos is in a box that has a width that is 3 in shorter than the height. the length of the base is 5in longer than the height. If the area of the ba

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Rosita's Christmas present from Calos is in a box that has a width that is 3 in shorter than the height. the length of the base is 5in longer than the height. If the area of the ba      Log On


   

Question 203754: Rosita's Christmas present from Calos is in a box that has a width that is 3 in shorter than the height. the length of the base is 5in longer than the height. If the area of the base is 84 square inches then what is the height of the package?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
W+=+%28h-3%29
L+=+%28h%2B5%29
The area of the base is found by:
A+=+L%2AW Substitute from above:
A+=+%28h%2B5%29%2A%28h-3%29 Substitute A = 84 sq.in.
84+=+h%5E2%2B2h-15 Subtract 84 from both sides.
h%5E2%2B2h-99+=+0 Factor the left side.
%28h-9%29%28h%2B11%29+=+0 Apply the zero product rule. If a%2Ab+=+0 then a+=+0 or b+=+0 or both.
h-9+=+0 or h%2B11+=+0 so that:
h+=+9 or cross%28h+=+-11%29 Discard the negative solution as height is a positive quantity.
h+=+9
The height of the package is 9 inches.