The area of a rectangle is 105mm^2. The length is six millimeters less than three times its width. Find the dimensions of the rectangle.
b) Write an equation using w for width.
c) What should the dimensions be?
l=
w=
b) Let w be the width of the rectangle. Then the length is 3w - 6.
c) The area of a rectangle is given by length times width, so we have (3w - 6) * w = 105.
Using this equation, we can find the width of the rectangle by solving for w:
3w^2 - 6w - 105 = 0.
This equation can be factored as (w - 7)(3w + 15) = 0.
So either w - 7 = 0 or 3w + 15 = 0.
If w - 7 = 0, then w = 7.
If 3w + 15 = 0, then 3w = -15, and w = -5.
Since a length and width cannot be negative, the width of the rectangle is 7.
To find the length, we substitute w = 7 into the equation for the length:
length = 3w - 6 = 3(7) - 6 = 21 - 6 = 15.
Therefore, the dimensions of the rectangle should be l = 15mm and w = 7mm.