Henry is building a front door. The height of the door is one foot more than twice its width. If the door is seven feet high, what is its width?
Am I suppose to use proportions
h = 2w + 1
7 = 2w + 1
7 - 1 = 2w + 1 - 1 ---> 6 = 2w
6/2 = 2w/2
3 = w or w = 3
Thank you.
You're welcome.
Yes, you can solve this problem using proportions. Proportions are an effective method for finding the missing value when two ratios are equal to each other. In this case, we can set up a proportion using the given information.
Let's say the width of the door is "x" feet. We know that the height of the door is seven feet, and it is one foot more than twice the width, which can be represented as 2x + 1.
We can set up the proportion as follows:
(width / height) = (width / height)
(x / 7) = [(2x + 1) / 7]
Now, we can cross-multiply and solve for "x":
7(2x + 1) = 7x
14x + 7 = 7x
7 = 7x - 14x
7 = -7x
Now, divide both sides by -7 to isolate "x":
7 / -7 = x
x = -1
The width of the door cannot be negative, so we have encountered an extraneous solution. In this case, it means that the door cannot be seven feet high with the given conditions.
Therefore, there might be an error in the problem statement, or some information is missing. It's always a good idea to double-check the given information and make sure all the details are accurate.