SOLUTION: I am having problems with two word problems: An open box will be made from a square piece of cardboard of length 26 inch by cutting 2 inch squares from the corners and folding

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I am having problems with two word problems: An open box will be made from a square piece of cardboard of length 26 inch by cutting 2 inch squares from the corners and folding      Log On


   

Question 10541: I am having problems with two word problems:

An open box will be made from a square piece of cardboard of length 26 inch by cutting 2 inch squares from the corners and folding up the sides. Find the volume of the box.

So if the length is 26 inches and you cut 2" squares off each end, then would the length then be 22?

So would the volume be l*w*h?
22 * 22* 2 = 968?


A ladder is leaning against the wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder if the distance of its top to the ground is 4 feet less than the length of the ladder.

I'm thinking the formula you use is:

a^2 + b^2 = c^2

So, a = c -3, and b = c-4

(c-2)^2 + (c-4)2 = c^2

c^2 -6c + 9 + c^2 - 8c + 16 = c^2

c^2 - 14c + 25 = 0

Then I'm stuck. I may be way off to begin with. Any help would be greatly appreciated. Thanks.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I have previously provided a solution to the first (box) problem and the answer you have given exactly matches mine...so, we are either both right or both wrong. Just kidding of course, the answer is 968 cubic inches.
2) You have done fine on this problem so far. Now you need to solve the quadratic equation for c, the length of the ladder.
c%5E2+-+14c+%2B+25+=+0 Since this won't factor you will want to use the quadratic formula: x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
c+=+%28-%28-14%29%2B-sqrt%28%28-14%29%5E2-4%281%29%2825%29%29%29%2F2%281%29
c+=+%28%2814%29%2B-sqrt%28196-100%29%29%2F2
c+=+%2814%2F2%29%2B-sqrt%2896%29%2F2
c+=+7%2B-sqrt%2816%2A6%29%2F2
c+=+7%2B-sqrt%286%29%284%2F2%29
c+=+7%2B-sqrt%286%29%282%29
Finally: c = 11.9 or c = 2.1
Discard the second solution as this would make the distance from the bottom of the ladder to the wall a negative number and this is meaningless.
So, the ladder is 11.9 feet long (Approximately. The result is 11.8989794856...)