Alright...so here, after we read the problem, we try to gather all given information: we have a rectangle (means both lengths (or the longest sides) are the same and the widths (the shorter sides) are the same), and the width of the rectangle is 4 units shorter than the length. So whatever the length is, the width is 4 units shorter than that. The area of the rectangle is 12 units. Ok, so what is the formula for the area of a rectangle? It is length X width.
Let's check to see what the question is asking us one more time: What is the width (in units)? That is our unknown amount.
Now that we've identified all our parts, let's see what kind of equation we can put together to solve for the missing value:
width = length - 4 or more mathematically, w = L - 4 (because the width is (and is mean equals) 4 units less than the length). Now, if the formula for area of a rectangle is l x w, or more mathematically,
A = l x w, so let's see what happens when we put all the information in:
12 ( the area) = L(the length) x(times or multiplied by) (L - 4)(the width) or more mathematically,
12 = L(L - 4) We have our equation, so let's distribute and solve!
12 = L2 - 4L (it's quadratic and how do we solve those? Factoring or quadratic formula!)
0 = L2 - 4L - 12 (we subtracted 12 from both sides)
0 = (L - 6)(L + 2) (we factored to discover our factors are -6 & +2)
L = 6 or L = -2 (setting each factor to 0 and solving yields us +6 and -2)
We disregard -2 because measurement cannot be negative so we know 6 is our answer
Hope this helps!!
