SOLUTION: A rectangular piece of cardboard is 15 inches longer than it is wide. If 5-inch squares are cut from each corner and the remaining piece folded up to form a box the volume of the b

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A rectangular piece of cardboard is 15 inches longer than it is wide. If 5-inch squares are cut from each corner and the remaining piece folded up to form a box the volume of the b      Log On


   

Question 926122: A rectangular piece of cardboard is 15 inches longer than it is wide. If 5-inch squares are cut from each corner and the remaining piece folded up to form a box the volume of the box is 1250 cubic inches. Find the dimensions of the piece of the box.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Try to draw a picture.

L for length, w for width.
L=w+15.
Height will be same as the edge of one of the removed squares, 5 inches.

Base of the box will be %28L-2%2A5%29%28w-2%2A5%29
%28w%2B15-2%2A5%29%28w-2%2A5%29
%28w%2B5%29%28w-10%29

The expression for the volume is 5%28w%2B5%29%28w-10%29.
This is the given volume value;
highlight%285%28w%2B5%29%28w-10%29=1250%29.
Solve that for w.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the width in inches of the cardboard
+x+%2B+15+ = the length in inches of the cardboard
-------------------
When the +5+ in squares are cut out, +10+ in
gets subtracted from both the length and width.
The height when the sides are folded up, is +5+ in
-------------------
+V+=+%28+x+-+10+%29%2A%28+x+%2B+15+-+10+%29%2A5+
+V+=+%28+x+-+10+%29%2A%28+x+%2B+5+%29%2A5+
+V+=++%28+x%5E2+-+10x+%2B+5x+-+50+%29%2A5+
+V+=+5x%5E2+-+25x+-+250+
+1250+=++5x%5E2+-+25x+-+250+
+250+=+x%5E2+-+5x+-+50+
+x%5E2+-+5x+-+300+=+0+
----------------------
Use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+-5+
+c+=+-300+
----------------
x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A%28-300%29+%29%29%2F%282%2A1%29+
x+=+%28+5+%2B-+sqrt%28+25+%2B+1200+%29%29%2F+2+
x+=+%28+5+%2B-+sqrt%28+1225+%29%29%2F+2+
+x+=+%28+5+%2B+35+%29+%2F+2+
+x+=+40%2F2+
+x+=+20+
+x+-+10+=+10+
+x+%2B+15+-+10+=+25+
The dimensions are:
10 x 25 x 5
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check:
+10%2A25%2A5+=+1250+
OK