SOLUTION: The length of a rectangle measures 4 cm less than 4 times the width. If the area is 31.0 cm^2, find the dimensions.

Question 122433: The length of a rectangle measures 4 cm less than 4 times the width. If the area is 31.0 cm^2, find the dimensions.
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
Let the length L and the width W then LW=31 (area is 31.0 cm^2)
and L=4W-4 (The length of a rectangle measures 4 cm less than 4 times the width)
then L=4(W-1) then 4(W-1)W=31 then 4W^2-4W-31=0 then W=(4+sqrt(16+16(31)))/8
or W=(4-sqrt(16+16(31)))/8 then solutions are W=(4+16sqrt(2))/8 or W=(4-16sqrt(2))/8 as the second solution is <0 the answer is W=(4+16sqrt(2))/8 if you simplify
W = 1/2+2sqrt(2) and
L = 4(W-1)= 4(-1/2+2sqrt(2)) = -2+8sqrt(2)
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