SOLUTION: the perimeter of a piece of cardboard is 34 inches. squares measuring 2 inches on a side are cut from each corner so that when sides are folded up, the diagonal of the resulting bo

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Question 1018209: the perimeter of a piece of cardboard is 34 inches. squares measuring 2 inches on a side are cut from each corner so that when sides are folded up, the diagonal of the resulting box has length 7 inches. what are the original dimensions of the cardboard?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Account for perimeter of the uncut rectangle:
2x%2B2y=34
highlight%28x%2By=17%29 when that equation simplified.

The dimensional measurements for the base surface after the four cut squares removed and flaps folded become %28x-2%2A2%29 and %28y-2%2A2%29.

The given diagonal value, through the THREE dimensions follows Pythagorean Theorem formula: highlight%28%28x-4%29%5E2%2B%28y-4%29%5E2%2B2%5E2=7%5E2%29, since the diagonal was given as 7.

The equations outlined in red color form a system to solve.
The 3-d diagonal equation should be simplified first...
system%28%28x-4%29%5E2%2B%28y-4%29%5E2=45%2Cx%2By=17%29, and go from there...