Question 128543
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.
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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
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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

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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.