A large painting in the style of Rubens is 3 feet longer than it is wide. If the wooden frame is 12 in wide and the area of the picture frame is 208 ft^2, find the dimensions of the painting.
So I know the width would be x and the length would be x+3
if I do 12x=208, I get 17.3333
I'm really not sure where to go with this can you please help?
Can you please explain the x-2 and x+1, I'm not sure how you got that.
Ummm the answer in the teacher's book says 11 ft by 14 ft. No idea where you guys got 54.5 and 51...
I got a different answer than all of you guys :P
HINT: To actually visualize the problem, draw it out! :)
Obviously the dimensions of the painting are: w and 3+w
We know that the frame is 12 in wide, aka 1 ft wide. And we also are given that the total area of the painting and the frame is 208ft^2.
We know that in order to get 208ft^2, we must multiply the length of the painting plus the width of the frame by the width of the painting plus the width of the frame. So therefore:
(3+w+2)(2w)
*Confused where we got the 2 from? We got 2 because you need to add the width of the frame to both sides of the width and both sides of the length.
Next we must distribute, then we will get: 6w+2w^2+4w or 2w^2+10w
Now we know that: 208=2w^2+10w
Our next step is to transfer this equation into Standard Form (ax^2+bx+c): 2w^2+10w-208= 0
Then use the Quadratic Formula to solve for x! (I can't type out the Quadratic Formula, so hopefully you already know what it is, if not just look it up)
You will get x= 8 or x=-13
Obviously, you cannot have a negative dimension so x=8 will be your answer.
The dimensions of the painting will be 8ft by 11ft.
Hope this helps!
the width of the painting would be x-2 feet (12 inches = 1 foot)
and the length would be x+1
(I have no idea what your equation 12x=208 is supposed to say)
area of whole picture = x(x+3)
area of painting = (x-2)(x+1)
the difference in those areas is 208
x(x+3) - (x-2)(x+1) = 208
solve
did you make a diagram?
if the outside width is x feet and you are coming in 12 inches or 1 foot on each side for the frame, isn't the inside width of the picture x - 2 feet
same for the length, which is x+3 on the outside.
come in 1 foot on each side and you have to subtract 2 feet from the original length.
Now what is (x+3) - 2 ?
Oh, these word problems make me feel so dense sometimes. Okay, so I got 54.5 and 51.5 as my demensions. Is that correct?
I got the same answer, and I verified it by
51.5x54.5 = 2806.75
49.5x52.5 = 2598.75
and 2806.75-2598.75 = 208