Problema Solution
The width of a rectangle is 6 centimeters less than twice it's length. It's perimeter is 18 square centimeters. Find the dimensions of the rectangle.
Answer provided by our tutors
let
w = the width of the rectangle
l = the length of the rectangle
the width of a rectangle is 6 centimeters less than twice it's length
w = 2l - 6
it's perimeter is 18 centimeters and it is equal to 2l + 2w = 2(l + w)
2(l + w) = 18 divide both sides by 2
l + w = 9
by solving the system of equations
w = 2l - 6
l + w = 9
we find
l = 5 cm
w = 4 cm
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the dimensions of the rectangle are 5 cm and 4 cm.
If instead of the perimeter we have the area of the rectangle equal to 18 square centimeters given we have
l*w = 18
and by plugin w = 2l - 6 in the above equation we have
(2l - 6)*l = 18
by solving the quadratic function we find and consider the positive roots thus
l = 4.85 cm
w = 2l - 6 = 3.7 cm
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