SOLUTION: I am stumped on two problems. Any help would be greatly apprecited. 1. An open-top box will be made from a square piece of cardboard of length 26-inch by cutting 2-inch squares

Question 128543: I am stumped on two problems. Any help would be greatly apprecited.
1. An open-top 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.
2. A ladder is leaning against a 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 topto the ground is 4 feet less than the length of the ladder.
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
A 26 SQUARE INCH PIECE OF CARDBOARD WITH 2 INCHES CUT OUT OF EACH CORNER & FOLDED TO MAKE AN OPEN TOP BOX IS:
22*22*2=968 IN^3
---------------------------------
(X-4)^2+(X-3)^2=X^2
X^2-8X+16+X^2-6X+9=X^2
X^2-14X+25=0
USING THE QUADRATIC EQUATION: WE GET:
X=(14+-SQRT[-14^2-4*1*25])/2*1
X=(14+-SQRT[196-100])/2
X=(14+-SQRT96)/2
X=(14+-9.8)/2
X=(14+9.8)/2
X=23.8/2
X=11.9 FEET IDS THE LENGTH OF THE LADDER.
PROOF:
(11.9-4)^2+(11.9-3)^2=11.9^2
7.9^2+8.9^2=141.61
62.41+79.21=141.61
141.61=141.61

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. An open-top 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.
-------------
Draw the picture including the 2" squares you cut out of each corner.
Label the remaining dimensions.
The height will be the 2-inch piece that you fold up to make the box
The base will be a square that is 22" by 22" because you cut 2" off each
end.
The volume will be 22*22*2 = 968 cubic inches
--------------------------------------------------
2. A ladder is leaning against a 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
----------
Draw the picture; Let the ladder length be "x"; base = x-3; height = x-4
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Use Pythagoras to get:
x^2 = (x-3)^2 + (x-4)^2
x^2 = x^2-6x+9 + x^2-8x+16
x^2-14x+25=0
x = [14 +- sqrt(14^2-4*25)]/2
x = [14 +- sqrt(96)]/2
x = [14 +- 4sqrt(6)]/2
Positive answer:
x = (7 + 2sqrt(6)]
x = 11.899... ft
Cheers,
Staln H.

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