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

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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:
A+=+h%2Aw but h = w+16 and A = 720, so making the appropriate substitutions, you get:
720+=+%28w%2B16%29%2Aw which, after some rearranging looks like:
w%5E2%2B16w-720+=+0 Do you see how we get this? Now you can factor this quadratic:
%28w-20%29%28w%2B36%29+=+0 which means that:
w+=+20 or w+=+-36 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.