SOLUTION: A rod of unknown length is used to measure the dimensions of a rectangular door. The rod is 4 ch'ih longer than the width of the door. The rod is 2 ch'ih longer than the height o

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Question 168855: A rod of unknown length is used to measure the dimensions of a rectangular door. The rod is 4 ch'ih longer than the width of the door. The rod is 2 ch'ih longer than the height of the door, ad the same length as the door's diagonal. What are the dimensions of the door?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the length of the rod x
given:
The width is x+-+4
The length is x+-+2
The diagonal is x
%28x+-+4%29%5E2+%2B+%28x+-+2%29%5E2+=+x%5E2
x%5E2+-+8x+%2B+16+%2B+x%5E2+-+4x+%2B+4+=+x%5E2
x%5E2+-+12x+%2B+20+=+0
%28x+-+10%29%2A%28x+-+2%29+=+0
There are 2 solutions
x+=+2
This is impossible because x+-+2+=+0 and x+-+4+=+-2
x+=+10 answer
x+-+2+=+8
x+-+4+=+6
The dimensions of the door are 6x8
check:
%28x+-+4%29%5E2+%2B+%28x+-+2%29%5E2+=+x%5E2
%2810+-+4%29%5E2+%2B+%2810+-+2%29%5E2+=+10%5E2
6%5E2+%2B+8%5E2+=+10%5E2
36+%2B+64+=+100
100+=+100
OK