The length of a rectangle is 12 centimeters less than its width. What are the dimensions of the rectangle if it’s area is 85 square centimeters?
+129918 Let the width = W
Let the length, L = W - 12
Area = W * L
So.....
85 = W ( W - 12) simplify
85 = W^2 - 12W rearrange as
W^2 -12W - 85 = 0 factor
(W+ 5) (W -17) = 0
Setting both factors to 0 and solving for W produces
W = - 5 (reject)
W = 17 (accept)
And L = W - 12 = 17 - 12 = 5
+865 Let's make "x" the width.
Length = x-12.
Area of rectangle: Width * Length.
This means: x(x-12) = 85.
Simplifying that is: x^2 - 12x = 85.
Rearranging it: x^2 - 12x - 85 = 0.
Factor it: (x+5)(x+17)-85 = 0
We can set both factors to 0 and solve for x:
x = -5 which doesn't work
x = 17 which works.
And for the Length: x - 12 = 17 -12 = 5.
I used the same method as CPhill though...
