SOLUTION: Ms. R wants to construct a house for her pet bunny out of a cardboard box. To make the house she is going to cut squares of side length x cm from each corner of a rectangular box (

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Question 1204562: Ms. R wants to construct a house for her pet bunny out of a cardboard box. To make the house she is going to cut squares of side length x cm from each corner of a rectangular box (see diagram below). The original dimensions of the uncut box are 51 cm by 45 cm. She wants the volume of the house to be 7175 cm^3.
Here is the link to the image: https://gyazo.com/b09d71efd4ffcfcc851e1ad3c3821622
a) Determine an equation that models this situation.
b) Find all possible dimensions of the box.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
If x is the edge length of each square to be removed then volume of the house is x%2851-2x%29%2845-2x%29. The given volume gives you x%2851-2x%29%2845-2x%29=7175.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The piece of cardboard is 51 x 45 cm, and squares with sides x are cut out of each corner. The dimensions of the bottom of the box are then 51-2x and 45-2x; and the height of the box is x.

Then the volume is length times width times height: V = (x)(51-2x)(45-2x)

We want that volume to be 7175 cubic centimeters.

ANSWER a):

%28x%29%2851-2x%29%2845-2x%29=7175

or

4x%5E3-192x%5E2%2B2295x=7175

A graphing calculator will show that there are two solutions; but with one of them the box is very deep with a much smaller base, making it not a good solution. That solution is also an irrational number, making finding the solution difficult without something like a graphing calculator.

For finding the reasonable solution, the easiest way is by looking at the factors of 7175. The difference in the dimensions of the cardboard is 6 cm, so we need to find factors of 7175 that differ by 6.

7175 = 25(287) = (5)(5)(7)(41) = (5)(35)(41)

This tells us that the squares cut out of each corner have side lengths of 5 cm, and the dimensions of the bottom of the box are 35 x 41 cm.

ANSWER b): 5 x 35 x 41 cm

or (approximately) 11.3265 x 22.347 x 28.347 cm