Asked by Natalie
a regular plot of land is designed so that its length is 6 meters more than its width. the diagonal of the land is 10 meters. to the nearest tenth of a meter, what are the dimensions of the land?
Answers
Answered by
Reiny
d^2 = x^2 + (x+6)^2 = 10^2
x^2 + x^2 + 12x + 36-100=0
x^2 + 6x -32 = 0
completing the square:
x^2 + 6x + 9 = 32+9
(x+3)^2 = 41
x + 3 = √41 , I ignored the negative answer
x = √41-3 = appr 3.403
one side is 3.403 , the other is 9.403
check:
3.403^2 + 9.403^2
= 99.996818
diagona = √... =9.99984
good enough
x^2 + x^2 + 12x + 36-100=0
x^2 + 6x -32 = 0
completing the square:
x^2 + 6x + 9 = 32+9
(x+3)^2 = 41
x + 3 = √41 , I ignored the negative answer
x = √41-3 = appr 3.403
one side is 3.403 , the other is 9.403
check:
3.403^2 + 9.403^2
= 99.996818
diagona = √... =9.99984
good enough
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