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?

1 Answer

Length = 24 m
Width = 18 m

Explanation:

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