The length of a rectangle is 6 cm more than the width, and the area is at least 91cm2. What are the possible dimensions of the rectangle?
6 years ago
Set Up an Aera formula for a rectangle:
Area = lw
width is some measurement, and length is that measurement + 6, l=w+6. Area is at least 91 cm, so an inequality is necessary. Substitute everything in:
91<w(w+6)
91<w2+6w
0<w2+6w-91
This quadratic can be factored
0<(w+13)(w-7)
So our two solutions are:
-13<w (Extraeous root because you cannot have a negative width of a rectangle)
7<w
So the width would have to be at least 7cm and the legth would have to be at least 13cm in order to have a rectagle with an area of at least 91cm2
6 years ago
Answered By Corey A
Set Up an Aera formula for a rectangle:
Area = lw
width is some measurement, and length is that measurement + 6, l=w+6. Area is at least 91 cm, so an inequality is necessary. Substitute everything in:
91<w(w+6)
91<w2+6w
0<w2+6w-91
This quadratic can be factored
0<(w+13)(w-7)
So our two solutions are:
-13<w (Extraeous root because you cannot have a negative width of a rectangle)
7<w
So the width would have to be at least 7cm and the legth would have to be at least 13cm in order to have a rectagle with an area of at least 91cm2