The length of a rectangular floor is 12 meters less than twice its width. If a diagonal of the rectangle is 30 meters, how do you find the length and width of the floor?

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Answer 1 · 2015-10-17T22:57:52

Length = 24 m
Width = 18 m

Width (W) = W
Length (L) = #2*W-12#
Diagonal (D) = 30

According to Pythagorean Theorem:

#30^2=W^2+(2.W-12)^2#

#900=W^2+4W^2-48W+12^2#

#900=5W^2-48W+144#

#5W^2-48W-756=0#

Solving the quadratic equation:

#Delta = 48^2-4*5*(-756) = 2304+15120=17424#

#W1=(-(-48)+sqrt(17424))/(2*5) = (48+132)/10#
#W1 = 18#

#W2=(-(-48)-sqrt(17424))/(2*5) = (48-132)/10#
#W2 = -8,4# (impossible)

#So, W = 18m#

#L=(2*18)-12 = 24m#