SOLUTION: good day! please help me with this word problem. thank you! The height of a painting is 16 inches greater than the width and the area of the painting is 720 square inches. Can i

Question 640394: good day! please help me with this word problem. thank you!
The height of a painting is 16 inches greater than the width and the area of the painting is 720 square inches. Can it be hung in a 2 feet by 4 feet wall space?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
To answer this question, you'll need to find the height and width of the painting. Let h = the height and w = the width:
The area of the rectangular painting is expressed by:
but h = w+16 and A = 720, so making the appropriate substitutions, you get:
which, after some rearranging looks like:
Do you see how we get this? Now you can factor this quadratic:
which means that:
or Discard the negative solution as the width must be a positive quantity.
So the width is 20 inches and the height is 36 (20+16) inches.
Convert to feet:
Width = 1ft 8in.
Height = 3 ft.
So you can see that the painting will fit in the allocated space.
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