Answer: The width is 7 units.
Step-by-step explanation:
What we know:
- Area of the rectangle is 56
- The length of a rectangle is 1 unit more than the width
I will be using the variable w to represent the width.
Let's write it out:
Length = w + 1
Width = w
We know that the area is length x width
So the equation is (w + 1) x w = 56
Let's simplify this equation!
w^2 + w = 56
Now we need to find the solutions of this equation and see which one works.
Rewrite the eqaution:
w^2 + w - 56 = 0
Factor, find two factors of -56 whose sum equals the coefficient of the middle term (w):
-7, 8
Rewrite:
w^2 - 7w + 8w - 56 = 0
This part is a little tricky for me to explain, I apologize in advance for any confusion, but you want to do a little something like this:
(w+8) x (w-7) = 0
Now we solve both terms by = 0 seperately:
w + 8 = 0
= -8
w - 7 = 0
w = 7
Solutions:
w = 7, -8
Now that we have our solutions, we can choose which one best fits our scenario. In this case, <u>7 will fit the best.</u>
To check this, we just plug it all in!
Length: 7 + 1 = 8
Width: 7
Area is <u>length x width.</u> So now we multiply:
8 x 7 = 56.
The width of this rectangle is 7 units.
